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Relevant bibliographies by topics / Wrapped Fukaya category

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Academic literature on the topic 'Wrapped Fukaya category'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Wrapped Fukaya category"

1

Lekili, Yankı, and Alexander Polishchuk. "Homological mirror symmetry for higher-dimensional pairs of pants." Compositio Mathematica 156, no. 7 (2020): 1310–47. http://dx.doi.org/10.1112/s0010437x20007150.

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Using Auroux’s description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of $k+1$ generic hyperplanes in $\mathbb{CP}^{n}$, for $k\geqslant n$, with respect to certain stops in terms of the endomorphism algebra of a generating set of objects. The stops are chosen so that the resulting algebra is formal. In the case of the complement of $n+2$ generic hyperplanes in $\mathbb{C}P^{n}$ ($n$-dimensional pair of pants), we show that our partial wrapped Fukaya category is equivalent to a certain categorical resolut

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2

Abouzaid, Mohammed. "On the wrapped Fukaya category and based loops." Journal of Symplectic Geometry 10, no. 1 (2012): 27–79. http://dx.doi.org/10.4310/jsg.2012.v10.n1.a3.

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3

Ritter, Alexander F., and Ivan Smith. "The monotone wrapped Fukaya category and the open-closed string map." Selecta Mathematica 23, no. 1 (2016): 533–642. http://dx.doi.org/10.1007/s00029-016-0255-9.

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4

Cooper, Benjamin, and Peter Samuelson. "THE HALL ALGEBRAS OF SURFACES I." Journal of the Institute of Mathematics of Jussieu 19, no. 3 (2018): 971–1028. http://dx.doi.org/10.1017/s1474748018000324.

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We study the derived Hall algebra of the partially wrapped Fukaya category of a surface. We give an explicit description of the Hall algebra for the disk with $m$ marked intervals and we give a conjectural description of the Hall algebras of all surfaces with enough marked intervals. Then we use a functoriality result to show that a graded version of the HOMFLY-PT skein relation holds among certain arcs in the Hall algebras of general surfaces.

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5

Ganatra, Sheel, John Pardon, and Vivek Shende. "Sectorial descent for wrapped Fukaya categories." Journal of the American Mathematical Society, October 24, 2023. http://dx.doi.org/10.1090/jams/1035.

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We develop a set of tools for doing computations in and of (partially) wrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf) property for the wrapped Fukaya category with respect to so-called Weinstein sectorial coverings and (2) that the partially wrapped Fukaya category of a Weinstein manifold with respect to a mostly Legendrian stop is generated by the cocores of the critical handles and the linking disks to the stop. We also prove (3) a ‘stop removal equals localization’ result, and (4) that the Fukaya–Seidel category of a Lefschetz fibration with Liouville fiber is ge

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6

Bae, Youngjin, Seonhwa Kim, and Yong-Geun Oh. "A wrapped Fukaya category of knot complement." Mathematische Zeitschrift 304, no. 2 (2023). http://dx.doi.org/10.1007/s00209-023-03285-8.

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7

Bae, Hanwool, Wonbo Jeong, and Jongmyeong Kim. "Calabi–Yau structures on Rabinowitz Fukaya categories." Journal of Topology 17, no. 4 (2024). http://dx.doi.org/10.1112/topo.12361.

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AbstractIn this paper, we prove that the derived Rabinowitz Fukaya category of a Liouville domain of dimension is ‐Calabi–Yau, assuming that the wrapped Fukaya category of admits an at most countable set of Lagrangians that generate it and satisfy some finiteness condition on morphism spaces between them.

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8

Groman, Yoel. "The wrapped Fukaya category for semi-toric Calabi–Yau." Journal of the European Mathematical Society, May 24, 2024. http://dx.doi.org/10.4171/jems/1466.

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9

Bosshard, Valentin. "Lagrangian cobordisms in Liouville manifolds." Journal of Topology and Analysis, April 18, 2022, 1–55. http://dx.doi.org/10.1142/s1793525322500030.

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Floer theory for Lagrangian cobordisms was developed by Biran and Cornea in a series of papers [Lagrangian cobordism. I, J. Amer. Math. Soc. 26 (2013) 295–340; Lagrangian cobordism and Fukaya categories, Geom. Funct. Anal. 24 (2014) 1731–1830; Cone-decompositions of Lagrangian cobordisms in Lefschetz fibrations, Selecta Math. 23 (2017) 2635–2704] to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. This paper explains how to use the language of stops to study Lagrangian cobordisms in Liouville manifolds and the associated exact triangles in the d

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10

Auroux, Denis, and Ivan Smith. "Fukaya categories of surfaces, spherical objects and mapping class groups." Forum of Mathematics, Sigma 9 (2021). http://dx.doi.org/10.1017/fms.2021.21.

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Abstract We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least $2$ whose Chern character represents a nonzero Hochschild homology class is quasi-isomorphic to a simple closed curve equipped with a rank $1$ local system. (The homological hypothesis is necessary.) This largely answers a question of Haiden, Katzarkov and Kontsevich. It follows that there is a natural surjection from the autoequivalence group of the Fukaya category to the mapping class group. The proofs appeal to and illustrate numerous recent developments: quiver algebra models

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Dissertations / Theses on the topic "Wrapped Fukaya category"

1

Ganatra, Sheel (Sheel Chandrakant). "Symplectic cohomology and duality for the wrapped Fukaya Category." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/73362.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 313-315).<br>Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that natural geometric maps from the Hochschild homology of W to symplectic cohomology and from symplectic cohomology to the Hochschild cohomology of W are isomorphisms, in a manner compatible with ring and module structures. This

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2

Zhang, Zhongyi. "On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold." Thesis, 2020. https://doi.org/10.7916/d8-9xbk-hq04.

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We introduce an $A_\infty$ map from the cubical chain complex of the based loop space of Lagrangian submanifolds with Legendrian boundary in a Liouville Manifold $C_{*}(\Omega_{L} \Lag)$ to wrapped Floer cohomology of Lagrangian submanifold $\CW^{-*}(L,L)$. In the case of a cotangent bundle and a Lagrangian co-fiber, the composition of our map with the map from $\CW^{-*}(L,L) \to C_{*}(\Omega_q Q) $ as defined in \cite{Ab12} shows that this map is split surjective.

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Books on the topic "Wrapped Fukaya category"

1

Zhang, Zhongyi. On Wrapped Fukaya Category and loop space of Lagrangians in a Liouville Manifold. [publisher not identified], 2020.

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