Braid-positive Legendrian links

Any link that is the closure of a positive braid has a natural Legendrian representative. These representatives were introduced in an earlier paper, where their Chekanov-Eliashberg contact homology was also evaluated. In this paper, we rephrase and improve that computation using a matrix representat...

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Bibliographic Details
Published inInternational Mathematics Research Notices Vol. 2006
Format Journal Article
LanguageEnglish
Published Hindawi Publishing Corporation 2006
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Summary:Any link that is the closure of a positive braid has a natural Legendrian representative. These representatives were introduced in an earlier paper, where their Chekanov-Eliashberg contact homology was also evaluated. In this paper, we rephrase and improve that computation using a matrix representation. In particular, we present a way of finding all augmentations of such Legendrians, construct an augmentation which is also a ruling, and find surprising links to LU-decompositions and Gröbner bases.
Bibliography:ark:/67375/HXZ-5M7X8HGJ-L
istex:779676271608E595E708361C5D2B8298444E2E14
PII:S1073792806148746
ISSN:1073-7928
1687-1197
DOI:10.1155/IMRN/2006/14874