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

TL;DR

This paper constructs infinitely many irreducible integer homology 3-spheres that are not L-spaces and whose fundamental groups lack nontrivial tenilde{PSL_2(\u211d)} representations, advancing understanding of their geometric and algebraic properties.

Contribution

It provides new examples of non L-space integer homology 3-spheres with fundamental groups without nontrivial tenilde{PSL_2(\u211d)} representations, expanding the class of known such manifolds.

Findings

Existence of infinitely many such 3-spheres.

Fundamental groups lack nontrivial tenilde{PSL_2(\u211d)} representations.

These examples are irreducible and non L-space.

Abstract

This paper gives infinitely many examples of non L-space irreducible integer homology 3-spheres whose fundamental groups do not have nontrivial $\widetilde{PSL_2(\mathbb{R})}$ representations.