DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bae, Youngjin | - |
dc.contributor.author | Kim, Seonhwa | - |
dc.contributor.author | Oh, Yong-Geun | - |
dc.date.accessioned | 2022-03-16T05:20:06Z | - |
dc.date.available | 2022-03-16T05:20:06Z | - |
dc.date.created | 2021-10-21 | - |
dc.date.issued | 2021-02 | - |
dc.identifier.issn | 1093-6106 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/110878 | - |
dc.description.abstract | This is a sequel to the authors' article [BKO]. We consider a hyperbolic knot K in a closed 3-manifold M and the cotangent bundle of its complement M \ K. We equip M \ K with a hyperbolic metric h and its cotangent bundle T* (M\K) with the induced kinetic energy Hamiltonian H-h = 1/2 vertical bar p vertical bar 2/h and Sasakian almost complex structure J(h), and associate a wrapped Fukaya category to T* (M \ K) whose wrapping is given by H-h. We then consider the conormal nu*T of a horo-torus T as its object. We prove that all non-constant Hamiltonian chords are transversal and of Morse index 0 relative to the horo-torus T, and so that the structure maps satisfy (m) over tilde (k) = 0 unless k not equal 2 and an A(infinity)-algebra associated to nu*T is reduced to a noncommutative algebra concentrated to degree 0. We prove that the wrapped Floer cohomology HW (nu*T; H-h) with respect to H-h is well-defined and isomorphic to the Knot Floer cohomology HW (partial derivative(infinity)(M / K)) that was introduced in [BKO] for arbitrary knot K subset of M. We also define a reduced cohomology, denoted by (HW) over tilde (d) (partial derivative(infinity)(M / K)), by modding out constant chords and prove that if (HW) over tilde (d) (partial derivative(infinity)(M / K)) not equal 0 for some d >= 1, then K cannot be hyperbolic. On the other hand, we prove that all torus knots have (HW) over tilde (1) (partial derivative(infinity)(M / K)) not equal 0. | - |
dc.language | English | - |
dc.publisher | International Press | - |
dc.relation.isPartOf | Asian Journal of Mathematics | - |
dc.title | FORMALITY OF FLOER COMPLEX OF THE IDEAL BOUNDARY OF HYPERBOLIC KNOT COMPLEMENT | - |
dc.type | Article | - |
dc.identifier.doi | 10.4310/AJM.2021.v25.n1.a7 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | Asian Journal of Mathematics, v.25, no.1, pp.117 - 176 | - |
dc.identifier.wosid | 000704396000007 | - |
dc.citation.endPage | 176 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 117 | - |
dc.citation.title | Asian Journal of Mathematics | - |
dc.citation.volume | 25 | - |
dc.contributor.affiliatedAuthor | Oh, Yong-Geun | - |
dc.identifier.scopusid | 2-s2.0-85125506429 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.type.docType | Article | - |
dc.subject.keywordPlus | HOMOLOGY | - |
dc.subject.keywordAuthor | Hyperbolic knots | - |
dc.subject.keywordAuthor | Knot Floer algebra | - |
dc.subject.keywordAuthor | horo-torus | - |
dc.subject.keywordAuthor | formality | - |
dc.subject.keywordAuthor | totally geodesic triangle | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
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