Algebraic & Geometric Topology

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

Xinghua Gao

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

Article information

Algebr. Geom. Topol., Volume 17, Number 4 (2017), 2511-2522.

Received: 5 October 2016
Revised: 7 January 2017
Accepted: 20 January 2017
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

L–space left orderability homology sphere $\mathrm{SL}_2(\mathbb{R})$ representation


Gao, Xinghua. Non-L–space integral homology $3$–spheres with no nice orderings. Algebr. Geom. Topol. 17 (2017), no. 4, 2511--2522. doi:10.2140/agt.2017.17.2511.

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