## Geometry & Topology

### Floer homology and covering spaces

#### 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 $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.

#### Article information

Source
Geom. Topol., Volume 22, Number 5 (2018), 2817-2838.

Dates
Accepted: 5 November 2017
First available in Project Euclid: 26 March 2019

https://projecteuclid.org/euclid.gt/1553565673

Digital Object Identifier
doi:10.2140/gt.2018.22.2817

Mathematical Reviews number (MathSciNet)
MR3811772

Zentralblatt MATH identifier
1395.57041

Subjects
Primary: 57R58: Floer homology
Secondary: 57M10: Covering spaces 57M60: Group actions in low dimensions

#### Citation

Lidman, Tye; Manolescu, Ciprian. Floer homology and covering spaces. Geom. Topol. 22 (2018), no. 5, 2817--2838. doi:10.2140/gt.2018.22.2817. https://projecteuclid.org/euclid.gt/1553565673

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