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A wrapped Fukaya category of knot complement

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Title
A wrapped Fukaya category of knot complement
Author(s)
Bae, Youngjin; Kim, Seonhwa; Yong-Geun Oh
Publication Date
2023-06
Journal
MATHEMATISCHE ZEITSCHRIFT, v.304, no.2
Publisher
SPRINGER HEIDELBERG
Abstract
This is the first of a series of two articles where we construct a version of wrapped Fukaya category WF(M\K; H-g0) of the cotangent bundle T *(M\K) of the knot complement M\K of a compact 3-manifold M , and do some calculation for the case of hyperbolic knots K ? M. For the construction, we use the wrapping induced by the kinetic energy Hamiltonian H-g0 associated to the cylindrical adjustment (g0) on M\K of a smooth metric g defined on M. We then consider the torus T = ?N(K) as an object in this category and its wrapped Floer complex CW*(?*T; H-g0) where N(K) is a tubular neighborhood of K ? M. We prove that the quasi-equivalence class of the category and the quasi-isomorphism class of the A00 algebra CW*(?*T; H-g0) are independent of the choice of cylindrical adjustments of such metrics depending only on the isotopy class of the knot K in M. In a sequel (Bae et al. in Asian J Math 25(1):117-176, 2019), we give constructions of a wrapped Fukaya category WF(M\K; H-h) for hyperbolic knot K and of A00 algebra CW*(?*T; H-h) directly using the hyperbolic metric h on M\K , and prove a formality result for the asymptotic boundary of (M\K , h).
URI
https://pr.ibs.re.kr/handle/8788114/13727
DOI
10.1007/s00209-023-03285-8
ISSN
0025-5874
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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