On cobordism maps on periodic Floer homology

Chen, Guanheng

doi:10.2140/agt.2021.21.1

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On cobordism maps on periodic Floer homology

Guanheng Chen

Algebraic & Geometric Topology 21 (2021) 1–103

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.

Keywords

periodic Floer homology, Seiberg–Witten Floer homology, cobordism maps

Mathematical Subject Classification 2010

Primary: 57R58

Secondary: 53D40

References

Publication

Received: 23 May 2018

Revised: 29 March 2020

Accepted: 30 March 2020

Published: 25 February 2021

Authors

Guanheng Chen
Department of Mathematics The Chinese University of Hong Kong Hong Kong	School of Mathematical Sciences University of Adelaide Adelaide SA Australia

Volume 21, issue 1 (2021)