Floer homology and covering spaces
Geometric Topology
2017-11-08 v2
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 p^n-sheeted regular cover that is a Z/pZ-L-space (for p prime), then Y is a Z/pZ-L-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
Cite
@article{arxiv.1603.00584,
title = {Floer homology and covering spaces},
author = {Tye Lidman and Ciprian Manolescu},
journal= {arXiv preprint arXiv:1603.00584},
year = {2017}
}
Comments
15 pages; to appear in Geometry & Topology