A complete knot invariant from contact homology
成果类型：
Article
署名作者：
Ekholm, Tobias; Ng, Lenhard; Shende, Vivek
署名单位：
Uppsala University; Royal Swedish Academy of Sciences; Mittag-Leffler Institute; Duke University; University of California System; University of California Berkeley
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-017-0761-1
发表日期：
2018
页码：
1149-1200
关键词：
摘要：
We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The enhancement consists of the (fully noncommutative) Legendrian contact homology associated to the union of the conormal torus of the knot and a disjoint cotangent fiber sphere, along with a product on a filtered part of this homology. As a corollary, we obtain a new, holomorphic-curve proof of a result of the third author that the Legendrian isotopy class of the conormal torus is a complete knot invariant.