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Non-L–space integral homology $3$–spheres with no nice orderings

Xinghua Gao

Algebraic & Geometric Topology 17 (2017) 2511–2522
Abstract

We give infinitely many examples of non-L–space irreducible integer homology 3–spheres whose fundamental groups do not have nontrivial PSL˜2() representations.

Keywords
L–space, left orderability, homology sphere, $\mathrm{SL}_2(\mathbb{R})$ representation
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57M25, 57M27
References
Publication
Received: 5 October 2016
Revised: 7 January 2017
Accepted: 20 January 2017
Published: 3 August 2017
Authors
Xinghua Gao
Department of Mathematics
University of Illinois, Urbana-Champaign
Urbana, IL 61801
United States