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2021 On cobordism maps on periodic Floer homology
Guanheng Chen
Algebr. Geom. Topol. 21(1): 1-103 (2021). DOI: 10.2140/agt.2021.21.1

Abstract

We investigate the cobordism maps on periodic Floer homology (PFH). In the first part of the paper, we define the cobordism maps on PFH via Seiberg–Witten theory as well as the isomorphism between PFH and Seiberg–Witten cohomology. Furthermore, we show that the maps satisfy the holomorphic curve axiom. In the second part of the paper, we give an alternative definition of these maps by using holomorphic curves, provided that the symplectic cobordisms are Lefschetz fibrations satisfying certain nice conditions. Under certain additional monotonicity assumptions, we show that these two definitions are equivalent.

Citation

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Guanheng Chen. "On cobordism maps on periodic Floer homology." Algebr. Geom. Topol. 21 (1) 1 - 103, 2021. https://doi.org/10.2140/agt.2021.21.1

Information

Received: 23 May 2018; Revised: 29 March 2020; Accepted: 30 March 2020; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.2140/agt.2021.21.1

Subjects:
Primary: 57R58
Secondary: 53D40

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 1 • 2021
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