Rank p − 1 mod-p H-spaces
Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite p -local H -spaces of rank l < p − 1. The first construction goes through when l = p − 1 and we show the second does as well. However, the space produced need not be an H -space. We gi...
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Published in | Israel journal of mathematics Vol. 194; no. 2; pp. 641 - 688 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Boston
Springer US
01.03.2013
|
Subjects | |
Online Access | Get full text |
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Abstract | Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite
p
-local
H
-spaces of rank
l
<
p
− 1. The first construction goes through when
l
=
p
− 1 and we show the second does as well. However, the space produced need not be an
H
-space. We give a criterion for when an
H
-space is obtained. In the special case of rank 2 mod-3
H
-spaces, we also give a practical test for when the criterion holds, and use this to give many new examples of finite
H
-spaces. |
---|---|
AbstractList | Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite
p
-local
H
-spaces of rank
l
<
p
− 1. The first construction goes through when
l
=
p
− 1 and we show the second does as well. However, the space produced need not be an
H
-space. We give a criterion for when an
H
-space is obtained. In the special case of rank 2 mod-3
H
-spaces, we also give a practical test for when the criterion holds, and use this to give many new examples of finite
H
-spaces. |
Author | Harper, John Mimura, Mamoru Theriault, Stephen Wu, Jie Grbić, Jelena |
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Cites_doi | 10.1007/BF02760533 10.1017/S0305004100061971 10.2307/2007107 10.1007/BF02566956 10.1007/BF01404323 10.1007/s11856-010-0068-z 10.1016/0040-9383(88)90011-0 10.1090/S0894-0347-08-00623-1 10.4007/annals.2008.167.95 10.1090/conm/293/04943 10.4153/CJM-1976-029-0 10.1016/0040-9383(79)90025-9 10.1007/s00209-005-0909-3 10.4153/CJM-1979-107-2 |
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Keywords | Bottom Cell Sphere Bundle Whitehead Product Homotopy Equivalent Homotopy Inverse |
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References | Wu (CR20) 2010; 178 Mimura (CR16) 1975 Selick, Wu (CR18) 2006; 256 Harper (CR10) 1982 CR19 Gray (CR8) 1988; 17 Ganea (CR6) 1969; 9 CR17 Zabrodsky (CR21) 1979; 33 Andersen, Grodal, Mℓler, Viruel (CR2) 2008; 167 Hagelgans (CR9) 1979; 31 Harper (CR12) 2010; 5 James (CR14) 1955; 62 Andersen, Grodal (CR1) 2009; 22 Harper (CR11) 2002 Ganea (CR5) 1965; 39 Hemmi (CR13) 2002 Mather (CR15) 1976; 28 Cooke, Harper, Zabrodsky (CR4) 1979; 18 Cohen, Neisendorfer (CR3) 1984 Gray (CR7) 1984; 96 T. Ganea (85_CR6) 1969; 9 J. Harper (85_CR12) 2010; 5 I. M. James (85_CR14) 1955; 62 K. Andersen (85_CR2) 2008; 167 M. Mather (85_CR15) 1976; 28 K. Andersen (85_CR1) 2009; 22 J. Wu (85_CR20) 2010; 178 85_CR19 B. Gray (85_CR7) 1984; 96 T. Ganea (85_CR5) 1965; 39 P. Selick (85_CR18) 2006; 256 N. Hagelgans (85_CR9) 1979; 31 F. R. Cohen (85_CR3) 1984 J. Harper (85_CR10) 1982 Y. Hemmi (85_CR13) 2002 M. Mimura (85_CR16) 1975 A. Zabrodsky (85_CR21) 1979; 33 J. Harper (85_CR11) 2002 B. Gray (85_CR8) 1988; 17 G. Cooke (85_CR4) 1979; 18 85_CR17 |
References_xml | – volume: 5 start-page: 173 year: 2010 end-page: 188 ident: CR12 article-title: − 1 publication-title: Kochi Journal of Mathematics contributor: fullname: Harper – ident: CR19 – volume: 33 start-page: 59 year: 1979 end-page: 72 ident: CR21 article-title: -3 publication-title: Israel Journal of Mathematics doi: 10.1007/BF02760533 contributor: fullname: Zabrodsky – start-page: 351 year: 1984 end-page: 359 ident: CR3 article-title: A construction of p-local H-spaces publication-title: Lecture Notes in Mathematics contributor: fullname: Neisendorfer – volume: 96 start-page: 95 year: 1984 end-page: 113 ident: CR7 article-title: Unstable families related to the image of J publication-title: Mathematical Proceedings of the Cambridge Philosophical Society doi: 10.1017/S0305004100061971 contributor: fullname: Gray – volume: 62 start-page: 170 year: 1955 end-page: 197 ident: CR14 article-title: Reduced product spaces publication-title: Annals of Mathematics doi: 10.2307/2007107 contributor: fullname: James – volume: 39 start-page: 295 year: 1965 end-page: 322 ident: CR5 article-title: A generalization of the homology and homotopy suspension publication-title: Commentarii Mathematici Helvetici doi: 10.1007/BF02566956 contributor: fullname: Ganea – volume: 9 start-page: 185 year: 1969 end-page: 197 ident: CR6 article-title: Cogroups and suspensions publication-title: Inventiones Mathematicae doi: 10.1007/BF01404323 contributor: fullname: Ganea – start-page: 375 year: 1982 end-page: 388 ident: CR10 article-title: 2 -3 , in publication-title: CMS Conf. Proc. contributor: fullname: Harper – volume: 178 start-page: 349 year: 2010 end-page: 391 ident: CR20 article-title: ( −1)- publication-title: Israel Journal of Mathematics doi: 10.1007/s11856-010-0068-z contributor: fullname: Wu – ident: CR17 – volume: 17 start-page: 301 year: 1988 end-page: 310 ident: CR8 article-title: On the iterated suspension publication-title: Topology doi: 10.1016/0040-9383(88)90011-0 contributor: fullname: Gray – volume: 22 start-page: 387 year: 2009 end-page: 436 ident: CR1 article-title: The classification of 2-compact groups publication-title: Journal of the American Mathematical Society doi: 10.1090/S0894-0347-08-00623-1 contributor: fullname: Grodal – volume: 167 start-page: 95 year: 2008 end-page: 210 ident: CR2 article-title: The classification of p-compact groups for p odd publication-title: Annals of Mathematics doi: 10.4007/annals.2008.167.95 contributor: fullname: Viruel – start-page: 75 year: 2002 end-page: 88 ident: CR13 article-title: Unstable p-th order operation and H-spaces publication-title: Recent Progress in Homotopy Theory (Baltimore, MD, 2000) doi: 10.1090/conm/293/04943 contributor: fullname: Hemmi – year: 2002 ident: CR11 article-title: Secondary Cohomology Operations publication-title: Graduate Studies in Mathematics contributor: fullname: Harper – start-page: 273 year: 1975 end-page: 278 ident: CR16 article-title: On the mod p H-structures of spherical fibrations publication-title: Manifolds-Tokyo 1973 (Proc. 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Conf., Tokyo, 1973) contributor: fullname: Mimura – volume: 28 start-page: 225 year: 1976 end-page: 263 ident: CR15 article-title: Pull-backs in homotopy theory publication-title: Canadian Journal of Mathematics doi: 10.4153/CJM-1976-029-0 contributor: fullname: Mather – volume: 18 start-page: 349 year: 1979 end-page: 359 ident: CR4 article-title: Torsion free mod-p H-spaces of low rank publication-title: Topology doi: 10.1016/0040-9383(79)90025-9 contributor: fullname: Zabrodsky – volume: 256 start-page: 435 year: 2006 end-page: 451 ident: CR18 publication-title: Mathematische Zeitschrift doi: 10.1007/s00209-005-0909-3 contributor: fullname: Wu – volume: 31 start-page: 1293 year: 1979 end-page: 1306 ident: CR9 article-title: Local spaces with three cells as H-spaces publication-title: Canadian Journal of Mathematics doi: 10.4153/CJM-1979-107-2 contributor: fullname: Hagelgans – volume: 39 start-page: 295 year: 1965 ident: 85_CR5 publication-title: Commentarii Mathematici Helvetici doi: 10.1007/BF02566956 contributor: fullname: T. 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Snippet | Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite
p
-local
H
-spaces of rank
l
<
p
− 1. The... |
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SubjectTerms | Algebra Analysis Applications of Mathematics Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical |
Title | Rank p − 1 mod-p H-spaces |
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