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

Gao, Xinghua

doi:10.2140/agt.2017.17.2511

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

Xinghua Gao

Algebraic & Geometric Topology 17 (2017) 2511–2522

DOI: 10.2140/agt.2017.17.2511

Abstract

We give infinitely many examples of non-L–space irreducible integer homology $3$ –spheres whose fundamental groups do not have nontrivial ${\tilde{PSL}}_{2} (ℝ)$ 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

Volume 17, issue 4 (2017)