The Existence of a Meridional Curve in Closed Incompressible Surfaces in Fully Alternating Link Complements
Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S 3 contains a circle isotopic in the link complement to a meridian of the links. Based on this result, he was able to argue the hyperbolicity of non-split prime alternating links in S 3 ....
Saved in:
| Published in | Chinese annals of mathematics. Serie B Vol. 45; no. 1; pp. 73 - 80 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.01.2024
Springer Nature B.V School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in
S
3
contains a circle isotopic in the link complement to a meridian of the links. Based on this result, he was able to argue the hyperbolicity of non-split prime alternating links in
S
3
. Adams et al. showed that if
F
⊂
S
×
I L
is an essential torus, then
F
contains a circle which is isotopic in
S
×
I
\
L
to a meridian of
L
. The author generalizes his result as follows: Let
S
be a closed orientable surface,
L
be a fully alternating link in
S
×
I
. If
F
⊂
S
×
I
\
L
is a closed essential surface, then
F
contains a circle which is isotopic in
S
×
I
\
L
to a meridian of
L
. |
|---|---|
| AbstractList | 57M50%57N75; Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S3 contains a circle isotopic in the link complement to a meridian of the links.Based on this result,he was able to argue the hyperbolicity of non-split prime alternating links in S3.Adams et al.showed that if F ? S × I \ L is an essential torus,then F contains a circle which is isotopic in S × I \ L to a meridian of L.The author generalizes his result as follows:Let S be a closed orientable surface,L be a fully alternating link in S × I.If F ? S × I\L is a closed essential surface,then F contains a circle which is isotopic in S × I \ L to a meridian of L. Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S3 contains a circle isotopic in the link complement to a meridian of the links. Based on this result, he was able to argue the hyperbolicity of non-split prime alternating links in S3. Adams et al. showed that if F ⊂ S × I L is an essential torus, then F contains a circle which is isotopic in S × I \ L to a meridian of L. The author generalizes his result as follows: Let S be a closed orientable surface, L be a fully alternating link in S × I. If F ⊂ S × I \ L is a closed essential surface, then F contains a circle which is isotopic in S × I \ L to a meridian of L. Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S 3 contains a circle isotopic in the link complement to a meridian of the links. Based on this result, he was able to argue the hyperbolicity of non-split prime alternating links in S 3 . Adams et al. showed that if F ⊂ S × I L is an essential torus, then F contains a circle which is isotopic in S × I \ L to a meridian of L . The author generalizes his result as follows: Let S be a closed orientable surface, L be a fully alternating link in S × I . If F ⊂ S × I \ L is a closed essential surface, then F contains a circle which is isotopic in S × I \ L to a meridian of L . |
| Author | Lin, Wei |
| AuthorAffiliation | School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China |
| AuthorAffiliation_xml | – name: School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China |
| Author_xml | – sequence: 1 givenname: Wei surname: Lin fullname: Lin, Wei email: linwei201208@dlut.edu.cn organization: School of Mathematical Sciences, Dalian University of Technology |
| BookMark | eNp1kMtOwzAQRS0EEuXxAewssWAVmHFe9RJFvKQiFsDacuNJSes6xU6g_D2ugtQVq9mce3XnnLBD1zli7ALhGgHKm4CYASYgsgQAsmR7wCY4LSApRIGHbAIiF4nMpTxmJyEsATArc5iw1dsH8bttG3pyNfGu4Zo_k29N2zlteTX4L-Kt45XtAhn-5OpuvfEUQju3xF8H3-iawo64H6z94be2J-9037oFn7VuxavIW1qT68MZO2q0DXT-d0_Z-_3dW_WYzF4enqrbWVKnAH1Szou6RihBT6dGzuNfkBuDUmvZYImSZC10YQTo0uA8NVmeokiNKFFAhlOTnrKrsfdbu0a7hVp2Q9xkgwpbt1IkoiWI1rJIXo7kxnefA4V-jwopUplj1BYpHKnadyF4atTGt2vtfxSC2tlXo30Ve9XOvtrGjBgzIbJuQX7f_H_oF1woiLc |
| Cites_doi | 10.2307/1970594 10.1016/0166-8641(92)90130-R 10.2140/agt.2017.17.3375 10.1016/j.topol.2019.01.022 10.1016/0040-9383(94)90017-5 10.2140/pjm.1984.111.209 10.1016/S0166-8641(97)00014-X 10.1017/S0305004100072947 10.1017/S0305004100063465 |
| ClassificationCodes | 57M50%57N75 |
| ContentType | Journal Article |
| Copyright | The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2024 The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2024. Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
| Copyright_xml | – notice: The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2024 – notice: The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2024. – notice: Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
| DBID | AAYXX CITATION 2B. 4A8 92I 93N PSX TCJ |
| DOI | 10.1007/s11401-024-0004-x |
| DatabaseName | CrossRef Wanfang Data Journals - Hong Kong WANFANG Data Centre Wanfang Data Journals 万方数据期刊 - 香港版 China Online Journals (COJ) China Online Journals (COJ) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1860-6261 |
| EndPage | 80 |
| ExternalDocumentID | sxnk_e202401004 10_1007_s11401_024_0004_x |
| GroupedDBID | -01 -0A -5D -5G -BR -EM -SA -S~ -Y2 -~C .86 .VR 06D 0R~ 0VY 199 1N0 29B 2B. 2C. 2J2 2JN 2JY 2KG 2KM 2LR 2VQ 2~H 30V 4.4 406 408 40D 40E 5GY 5VR 5VS 5XA 5XB 6NX 78A 8TC 92E 92I 92M 92Q 93N 95- 95. 95~ 96X 9D9 9DA AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAXDM AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACUHS ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFGCZ AFLOW AFQWF AFUIB AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AZFZN B-. B0M BA0 BAPOH BDATZ BGNMA BSONS CAG CAJEA CCEZO CCVFK CHBEP COF CS3 CSCUP CW9 DDRTE DNIVK DPUIP DU5 EAD EAP EBLON EBS EIOEI EJD EMK EPL ESBYG EST ESX FA0 FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 H13 HF~ HG6 HMJXF HRMNR HZ~ IHE IJ- IKXTQ ITM IWAJR I~X I~Z J-C JBSCW JUIAU JZLTJ KOV LLZTM M4Y MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J P9R PF0 PT4 Q-- Q-0 QOS R-A R89 R9I REI ROL RPX RSV RT1 RWJ S.. S16 S1Z S27 S3B SAP SCL SCLPG SDD SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T8Q TCJ TGP TSG TUC TUS U1F U1G U2A U5A U5K UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 WSM YLTOR ZMTXR ZWQNP ~8M ~L9 AAPKM AAYXX ABBRH ABDBE ABFSG ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION ABRTQ 4A8 PSX |
| ID | FETCH-LOGICAL-c300t-7b6cc1070a88d9b14005dd19aa9f1719e9c2a6d20a7d1b3d453123d27120418d3 |
| IEDL.DBID | U2A |
| ISSN | 0252-9599 |
| IngestDate | Thu May 29 03:54:51 EDT 2025 Fri Jul 25 11:04:16 EDT 2025 Tue Jul 01 03:12:55 EDT 2025 Fri Feb 21 02:41:57 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Incompressible surfaces Meridionally incompressible 57M50 Fully alternating 57N75 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c300t-7b6cc1070a88d9b14005dd19aa9f1719e9c2a6d20a7d1b3d453123d27120418d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2923951252 |
| PQPubID | 2043818 |
| PageCount | 8 |
| ParticipantIDs | wanfang_journals_sxnk_e202401004 proquest_journals_2923951252 crossref_primary_10_1007_s11401_024_0004_x springer_journals_10_1007_s11401_024_0004_x |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 20240100 2024-01-00 20240101 2024 |
| PublicationDateYYYYMMDD | 2024-01-01 |
| PublicationDate_xml | – month: 1 year: 2024 text: 20240100 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationSubtitle | Chinese Annals of Mathematics, Series B |
| PublicationTitle | Chinese annals of mathematics. Serie B |
| PublicationTitleAbbrev | Chin. Ann. Math. Ser. B |
| PublicationTitle_FL | Chinese Annals of Mathematics,Series B |
| PublicationYear | 2024 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V – name: School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China |
| References | Lozanoand, Przytycki (CR8) 1985; 98 Adams (CR2) 2017; 17 Menasco (CR9) 1984; 33 Waldhausen (CR11) 1968; 87 CR5 Oertel (CR10) 1984; 111 Adams (CR1) 1994; 33 Adams, Albors-Riera, Haddock (CR3) 2019; 256 Adams, Brock, Bugbee (CR4) 1992; 46 Hayashi (CR7) 1995; 117 Fa (CR6) 1997; 80 C Adams (4_CR2) 2017; 17 C Adams (4_CR3) 2019; 256 M Lozanoand (4_CR8) 1985; 98 4_CR5 C Adams (4_CR4) 1992; 46 W Menasco (4_CR9) 1984; 33 F Waldhausen (4_CR11) 1968; 87 C Adams (4_CR1) 1994; 33 U Oertel (4_CR10) 1984; 111 C Hayashi (4_CR7) 1995; 117 H Fa (4_CR6) 1997; 80 |
| References_xml | – volume: 87 start-page: 56 year: 1968 end-page: 88 ident: CR11 article-title: On irreducible 3-manifolds which are sufficiently large publication-title: Ann. Math. doi: 10.2307/1970594 – volume: 46 start-page: 151 issue: 2 year: 1992 end-page: 165 ident: CR4 article-title: Almost alternating links publication-title: Topology Appl. doi: 10.1016/0166-8641(92)90130-R – volume: 17 start-page: 3375 issue: 6 year: 2017 end-page: 3397 ident: CR2 article-title: Generalized augmented alternating links and hyperbolic volumes publication-title: Algebr. Geom. Topol. doi: 10.2140/agt.2017.17.3375 – volume: 256 start-page: 262 year: 2019 end-page: 278 ident: CR3 article-title: Hyperbolicity of links in thickened surfaces publication-title: Topology Appl. doi: 10.1016/j.topol.2019.01.022 – volume: 33 start-page: 353 issue: 2 year: 1984 end-page: 369 ident: CR9 article-title: Closed incompressible surfaces in alternating knot and link complements publication-title: Topology – ident: CR5 – volume: 33 start-page: 353 issue: 2 year: 1994 end-page: 369 ident: CR1 article-title: Toroidally alternating knots and links publication-title: Topology doi: 10.1016/0040-9383(94)90017-5 – volume: 111 start-page: 209 issue: 1 year: 1984 end-page: 230 ident: CR10 article-title: Closed incompressible surfaces in complements of star links publication-title: Pacific J. Math. doi: 10.2140/pjm.1984.111.209 – volume: 80 start-page: 239 issue: 3 year: 1997 end-page: 249 ident: CR6 article-title: Incompressible pairwise incompressible surfaces in almost alternating knot complements publication-title: Topology Appl. doi: 10.1016/S0166-8641(97)00014-X – volume: 117 start-page: 113 issue: 1 year: 1995 end-page: 128 ident: CR7 article-title: Link with alternating diagrams on closed surfaces of positive genus publication-title: Math. Proc. Camb. Phil. Soc. doi: 10.1017/S0305004100072947 – volume: 98 start-page: 275 year: 1985 end-page: 299 ident: CR8 article-title: Incompressible surfaces in the exterior of a closed 3-braid I, surfaces with horizontal boundary components publication-title: Math. Proc. Camb. Phil. Soc. doi: 10.1017/S0305004100063465 – ident: 4_CR5 – volume: 256 start-page: 262 year: 2019 ident: 4_CR3 publication-title: Topology Appl. doi: 10.1016/j.topol.2019.01.022 – volume: 87 start-page: 56 year: 1968 ident: 4_CR11 publication-title: Ann. Math. doi: 10.2307/1970594 – volume: 117 start-page: 113 issue: 1 year: 1995 ident: 4_CR7 publication-title: Math. Proc. Camb. Phil. Soc. doi: 10.1017/S0305004100072947 – volume: 111 start-page: 209 issue: 1 year: 1984 ident: 4_CR10 publication-title: Pacific J. Math. doi: 10.2140/pjm.1984.111.209 – volume: 33 start-page: 353 issue: 2 year: 1994 ident: 4_CR1 publication-title: Topology doi: 10.1016/0040-9383(94)90017-5 – volume: 98 start-page: 275 year: 1985 ident: 4_CR8 publication-title: Math. Proc. Camb. Phil. Soc. doi: 10.1017/S0305004100063465 – volume: 80 start-page: 239 issue: 3 year: 1997 ident: 4_CR6 publication-title: Topology Appl. doi: 10.1016/S0166-8641(97)00014-X – volume: 33 start-page: 353 issue: 2 year: 1984 ident: 4_CR9 publication-title: Topology – volume: 17 start-page: 3375 issue: 6 year: 2017 ident: 4_CR2 publication-title: Algebr. Geom. Topol. doi: 10.2140/agt.2017.17.3375 – volume: 46 start-page: 151 issue: 2 year: 1992 ident: 4_CR4 publication-title: Topology Appl. doi: 10.1016/0166-8641(92)90130-R |
| SSID | ssj0014750 |
| Score | 2.3039658 |
| Snippet | Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in
S
3
contains a circle isotopic in the link... Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S3 contains a circle isotopic in the link... 57M50%57N75; Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S3 contains a circle isotopic in... |
| SourceID | wanfang proquest crossref springer |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 73 |
| SubjectTerms | Applications of Mathematics Mathematics Mathematics and Statistics Toruses |
| Title | The Existence of a Meridional Curve in Closed Incompressible Surfaces in Fully Alternating Link Complements |
| URI | https://link.springer.com/article/10.1007/s11401-024-0004-x https://www.proquest.com/docview/2923951252 https://d.wanfangdata.com.cn/periodical/sxnk-e202401004 |
| Volume | 45 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NS8MwFA-yXfQgfuJ0jhw8KYE0_Uhz3OamKPOig3kqSZMO2ehk3WT-9770Y1UQwVMPDQ_6fi_v-70idEXjMGHSlSTRiSBgjz0SSqaI4YmmSlEmpK3ojp6C-7H3MPEn5Rx3VnW7VyXJXFPXw242FiBgU_JJaAKOY9OH0N32cY1Zd1s68LhfJFZ8RoQvRFXK_I3ET2NUe5jbomg-ypMmMp1-szrDA7Rfuou4W-B7iHZMeoT2Rttdq9kxmgHSeLCxcAGAeJFgiUcgVzpP8uH-evlh8FuK-_NFZjQGhQAqIO9-VXODn9fLxHZl2RM2HP3E3XmZI0yn2Eaq2KqMosk8O0Hj4eClf0_KXyiQ2KV0RbgK4hgiPCrDUAsFn099rR0hpUgc7ggjYiYDzajk2lGu9uBKMlcz7jDqOaF2T1EjXaTmDGHXGB5wFXKIQDwDGLqKacHiQGjP6DhuoeuKl9F7sSkjqnciW8ZHwHhb7PaiTQu1K25H5aXJIgbOJjh8AFwL3VQI1K__IIZLkOrD2SadRYbZDW52J975vwheoF2WC4nNtLRRY7Vcm0vwPVaqg5rd3m1vaJ93r4-DTi57X3cU1A8 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NS8MwFA8yD-pB_MTp1Bw8KYE0_UhzHGNj6raLG-xWkiYd4uhk3WT-9770Y1UQwXNLoO_38t7vfRahOxqHCZOuJIlOBAF_7JFQMkUMTzRVijIhbUV3OAr6E-9p6k_LOe6s6navSpK5pa6H3WwsQMCn5JPQBIjjLnCB0KryhLW3pQOP-0VixWdE-EJUpczfjvjpjGqGuS2K5qM8aSLT2Tev0ztChyVdxO0C32O0Y9ITdDDc7lrNTtEbII27GwsXAIgXCZZ4CHql8yQf7qyXHwa_prgzX2RGYzAIYALy7lc1N_hlvUxsV5Z9w4ajn7g9L3OE6QzbSBVbk1E0mWdnaNLrjjt9Uv5CgcQupSvCVRDHEOFRGYZaKPh86mvtCClF4nBHGBEzGWhGJdeOcrUHV5K5mnGHUc8JtXuOGukiNRcIu8bwgKuQQwTiGcDQVUwLFgdCe0bHcRPdV7KM3otNGVG9E9kKPgLB22K3F22aqFVJOyovTRYxIJtA-AC4JnqoEKgf_3EYLkGqX8426VtkmN3gZnfiXf7rwFu01x8PB9HgcfR8hfZZrjA269JCjdVyba6Bh6zUTa53X1Hi0_w |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3da9swEBejg7E-lK5radps1UOfVkRlWbasx5Al9CtlsAX6ZiRLKqVBKXFS0v--J3_EG4xCny0OfL_Tfd8JoVNaZI6pWBFnnCRgjznJFNPECmeo1pRJFSq6k9v0Ysqv7pK75p3Tsu12b0uS9UxD2NLkl-dPxp13g28hLiBgX6qpaAJO5EcehoFBoKdssCkjcJHUSZaEEZlI2ZY1_0fiX8PUeZubAmk11uOd8vd_WaDxLtppXEc8qLH-gj5Yv4e2J5u9q-VX9Aio49E6QAdg4rnDCk9AxkyV8MPD1eLZ4gePh7N5aQ0G5QDqoOqE1TOLf68WLnRohRMhNH3Bg1mTL_T3OEStOKiPuuG83EfT8ejP8II0zymQIqZ0SYROiwKiPaqyzEgNv08TYyKplHSRiKSVBVOpYVQJE-nYcLieLDZMRIzyKDPxAdryc28PEY6tFanQmYBohFvAM9bMSFak0nBriqKHfrS8zJ_qrRl5tx85MD4HxofCN8_XPdRvuZ03F6jMGTie4PwBcD101iLQfX6DGG5A6g6Xa_-YWxa2uYX9eEfvIniCPv36Oc5vLm-vj9FnVslLSMD00dZysbLfwCVZ6u-V2L0CnTPYLw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+Existence+of+a+Meridional+Curve+in+Closed+Incompressible+Surfaces+in+Fully+Alternating+Link+Complements&rft.jtitle=%E6%95%B0%E5%AD%A6%E5%B9%B4%E5%88%8AB%E8%BE%91%EF%BC%88%E8%8B%B1%E6%96%87%E7%89%88%EF%BC%89&rft.au=Wei+LIN&rft.date=2024&rft.pub=School+of+Mathematical+Sciences%2CDalian+University+of+Technology%2CDalian+116024%2CLiaoning%2CChina&rft.issn=0252-9599&rft.volume=45&rft.issue=1&rft.spage=73&rft.epage=80&rft_id=info:doi/10.1007%2Fs11401-024-0004-x&rft.externalDocID=sxnk_e202401004 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fwww.wanfangdata.com.cn%2Fimages%2FPeriodicalImages%2Fsxnk-e%2Fsxnk-e.jpg |