## Geometry and Topology

•  Orders from $\widetilde{PSL_2(\mathbb{R})}$ Representations and Non-examples
•  01/26/2017
•  2:00 PM - 2:50 PM
•  C304 Wells Hall
•  Xinghua Gao, UIUC

It is still unknown for the case of rational homology 3-sphere whether the left-orderability of its fundamental group and it not be a Heegaard-Floer L-space are equivalent. Let $M$ be an integer homology 3-sphere. One way to study left-orderability of $\pi_1(M)$ is to construct a non-trivial representation from $\pi_1(M)$ to $\widetilde{PSL_2(\mathbb{R})}$. However this method does not always work. In this talk, I will give examples of non L-space irreducible integer homology 3-spheres whose fundamental groups do not have nontrivial $\widetilde{PSL_2(\mathbb{R})}$ representations.

## Contact

Department of Mathematics
Michigan State University