Department of Mathematics

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.

 

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