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Kim, Seonhwa
기하학 수리물리 연구단
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FORMALITY OF FLOER COMPLEX OF THE IDEAL BOUNDARY OF HYPERBOLIC KNOT COMPLEMENT

DC Field Value Language
dc.contributor.authorYOUNGJIN BAE-
dc.contributor.authorSEONHWA KIM-
dc.contributor.authorYONG-GEUN OH-
dc.date.accessioned2021-12-09T05:30:01Z-
dc.date.available2021-12-09T05:30:01Z-
dc.date.created2021-11-01-
dc.date.issued2021-01-01-
dc.identifier.issn1093-6106-
dc.identifier.urihttps://pr.ibs.re.kr/handle/8788114/10811-
dc.description.abstractThis 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.language영어-
dc.publisherINT PRESS BOSTON, INC-
dc.titleFORMALITY OF FLOER COMPLEX OF THE IDEAL BOUNDARY OF HYPERBOLIC KNOT COMPLEMENT-
dc.typeArticle-
dc.type.rimsART-
dc.identifier.wosid000704396000007-
dc.identifier.scopusid2-s2.0-85125506429-
dc.identifier.rimsid76619-
dc.contributor.affiliatedAuthorSEONHWA KIM-
dc.contributor.affiliatedAuthorYONG-GEUN OH-
dc.identifier.doi10.4310/AJM.2021.v25.n1.a7-
dc.identifier.bibliographicCitationASIAN JOURNAL OF MATHEMATICS, v.25, no.1, pp.117 - 176-
dc.relation.isPartOfASIAN JOURNAL OF MATHEMATICS-
dc.citation.titleASIAN JOURNAL OF MATHEMATICS-
dc.citation.volume25-
dc.citation.number1-
dc.citation.startPage117-
dc.citation.endPage176-
dc.description.journalClass1-
dc.description.journalClass1-
dc.description.isOpenAccessN-
dc.description.journalRegisteredClassscie-
dc.description.journalRegisteredClassscopus-
dc.relation.journalWebOfScienceCategoryMathematics, Applied-
dc.relation.journalWebOfScienceCategoryMathematics-
dc.subject.keywordPlusHOMOLOGY-
dc.subject.keywordAuthorHyperbolic knots-
dc.subject.keywordAuthorKnot Floer algebra-
dc.subject.keywordAuthorhoro-torus-
dc.subject.keywordAuthorformality-
dc.subject.keywordAuthortotally geodesic triangle-
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Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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