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Monoidal Structures on Fukaya Catego...

Niu, Yunpeng,

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Monoidal Structures on Fukaya Categories /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Monoidal Structures on Fukaya Categories // Yunpeng Niu.
Author:	Niu, Yunpeng,
Description:	1 electronic resource (71 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-12, Section: A.
Contained By:	Dissertations Abstracts International86-12A.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32043189
ISBN:	9798286435920

Monoidal Structures on Fukaya Categories /
Niu, Yunpeng,

Monoidal Structures on Fukaya Categories /Yunpeng Niu. - 1 electronic resource (71 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: A.

Homological mirror symmetry suggests that there should exist on the Fukaya category certain structures analogous to those known on the derived category of coherent sheaves. In 2010, A. Subotic constructed a natural monoidal structure on the generalized Donaldson-Fukaya category, mirror to the tensor product of coherent sheaves, when the symplectic manifold is equipped with a smooth Lagrangian fibration with a distinguished Lagrangian section. In this dissertation, we generalize this construction. Given a Lagrangian fibration with focus-focus type singularities on a symplectic 4-fold M, we associate geometrically an immersed Lagrangian correspondence from M x M to M. In the case of a generic elliptic K3, using this correspondence we construct an A∞ bi-functor on its Fukaya category, which is expected to give rise to a monoidal structure. This is partially based on joint work with M. Abouzaid and N. Bottman.

English

ISBN: 9798286435920Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Fukaya category

Monoidal Structures on Fukaya Categories /
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245 1 0 $a Monoidal Structures on Fukaya Categories / $c Yunpeng Niu.
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300 $a 1 electronic resource (71 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: A.
500 $a Advisors: Mclean, Mark; Fukaya, Kenji Committee members: Pardon, John; Laza, Radu; Abouzaid, Mohammed.
502 $b Ph.D. $c State University of New York at Stony Brook $d 2025.
520 $a Homological mirror symmetry suggests that there should exist on the Fukaya category certain structures analogous to those known on the derived category of coherent sheaves. In 2010, A. Subotic constructed a natural monoidal structure on the generalized Donaldson-Fukaya category, mirror to the tensor product of coherent sheaves, when the symplectic manifold is equipped with a smooth Lagrangian fibration with a distinguished Lagrangian section. In this dissertation, we generalize this construction. Given a Lagrangian fibration with focus-focus type singularities on a symplectic 4-fold M, we associate geometrically an immersed Lagrangian correspondence from M x M to M. In the case of a generic elliptic K3, using this correspondence we construct an A∞ bi-functor on its Fukaya category, which is expected to give rise to a monoidal structure. This is partially based on joint work with M. Abouzaid and N. Bottman.
546 $a English
590 $a School code: 0771
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Mathematics education. $3 641129
653 $a Fukaya category
653 $a Lagrangian fibration
653 $a Symplectic geometry
690 $a 0405
690 $a 0642
690 $a 0280
710 2 $a State University of New York at Stony Brook. $b Mathematics. $e degree granting institution. $3 3823091
720 1 $a Mclean, Mark $e degree supervisor.
720 1 $a Fukaya, Kenji $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12A.
790 $a 0771
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32043189