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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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.

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