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Floer homology and covering spaces

Tye Lidman and Ciprian Manolescu

Geometry & Topology 22 (2018) 2817–2838
Abstract

We prove a Smith-type inequality for regular covering spaces in monopole Floer homology. Using the monopole Floer/Heegaard Floer correspondence, we deduce that if a 3–manifold Y admits a pn–sheeted regular cover that is a pL–space (for p prime), then Y is a pL–space. Further, we obtain constraints on surgeries on a knot being regular covers over other surgeries on the same knot, and over surgeries on other knots.

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Keywords
Smith inequality, Seiberg–Witten, Heegaard Floer homology, virtually cosmetic, L–spaces
Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57M10, 57M60
References
Publication
Received: 12 February 2017
Accepted: 5 November 2017
Published: 1 June 2018
Proposed: András I Stipsicz
Seconded: Peter Ozsváth, Ian Agol
Authors
Tye Lidman
Department of Mathematics
North Carolina State University
Raleigh, NC
United States
Ciprian Manolescu
Department of Mathematics
UCLA
Los Angeles, CA
United States