Volume 17, issue 4 (2017)

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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 ${\stackrel{˜}{PSL}}_{2}\left(ℝ\right)$ representations.

Keywords
L–space, left orderability, homology sphere, $\mathrm{SL}_2(\mathbb{R})$ representation
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57M25, 57M27