Quantum cohomology as a deformation of symplectic cohomology

Matthew  Strom Borman; Nick Sheridan; Umut  Varolgunes

doi:10.1007/s11784-022-00965-6

Quantum cohomology as a deformation of symplectic cohomology

Matthew Strom Borman, Nick Sheridan, Umut Varolgunes

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement of a simple crossings symplectic divisor. We also prove rigidity results for the skeleton of the divisor complement.

Original language	English
Article number	48
Number of pages	72
Journal	Journal of Fixed Point Theory and Applications
Volume	24
Issue number	2
Early online date	7 Jun 2022
DOIs	https://doi.org/10.1007/s11784-022-00965-6
Publication status	Published - 7 Jun 2022

Keywords / Materials (for Non-textual outputs)

53D37
53D40

Access to Document

10.1007/s11784-022-00965-6

2108.08391Accepted author manuscript, 853 KB

https://arxiv.org/abs/2108.08391

1 Finished
1 Active

Homological mirror symmetry, Hodge theory, and symplectic topology
Sheridan, N.
EU government bodies
1/03/20 → 31/08/25
Project: Research
Homological mirror symmetry and symplectic topology
Sheridan, N.
Other (Learned Society)
1/08/18 → 31/12/22
Project: Research

Cite this

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title = "Quantum cohomology as a deformation of symplectic cohomology",

abstract = "We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement of a simple crossings symplectic divisor. We also prove rigidity results for the skeleton of the divisor complement.",

keywords = "53D37, 53D40",

author = "{Strom Borman}, Matthew and Nick Sheridan and Umut Varolgunes",

note = "Funding Information: N.S. is supported by a Royal Society University Research Fellowship, ERC Starting Grant 850713—HMS, and the Simons Collaboration on Homological Mirror Symmetry. U.V was partially supported by ERC Starting Grant 850713—HMS and is currently supported by TUBITAK CoCirculation2 Grant number 121C034. We are grateful to Yoel Groman, Ana Rita Pires, Paul Seidel, Ivan Smith, and Dmitry Tonkonog for helpful conversations; and to Dan Pomerleano for explaining Conjecture to us. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

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AU - Strom Borman, Matthew

AU - Sheridan, Nick

AU - Varolgunes, Umut

N1 - Funding Information: N.S. is supported by a Royal Society University Research Fellowship, ERC Starting Grant 850713—HMS, and the Simons Collaboration on Homological Mirror Symmetry. U.V was partially supported by ERC Starting Grant 850713—HMS and is currently supported by TUBITAK CoCirculation2 Grant number 121C034. We are grateful to Yoel Groman, Ana Rita Pires, Paul Seidel, Ivan Smith, and Dmitry Tonkonog for helpful conversations; and to Dan Pomerleano for explaining Conjecture to us. Publisher Copyright: © 2022, The Author(s).

PY - 2022/6/7

Y1 - 2022/6/7

N2 - We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement of a simple crossings symplectic divisor. We also prove rigidity results for the skeleton of the divisor complement.

AB - We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement of a simple crossings symplectic divisor. We also prove rigidity results for the skeleton of the divisor complement.

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KW - 53D40

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DO - 10.1007/s11784-022-00965-6

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SN - 1661-7738

VL - 24

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 2

M1 - 48

ER -

Quantum cohomology as a deformation of symplectic cohomology

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Keywords / Materials (for Non-textual outputs)

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Projects

Homological mirror symmetry, Hodge theory, and symplectic topology

Homological mirror symmetry and symplectic topology

Cite this