Taut foliations on graph manifolds

Taut foliations on graph manifolds

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Liam Watson, University of Glasgow
Fine Hall 314

An L-space is a rational homology sphere with simplest possible Heegaard Floer homology. Ozsváth and Szabó have shown that if a closed, connected, orientable three-manifold has a coorientable taut foliation then it is not an L-space. I will explain how to prove the converse to this statement when restricting to graph manifolds. Combined with work of Boyer and Clay, this leads to an equivalence between graph manifold L-spaces and graph manifolds with non-left-orderable fundamental group. This is joint work with J. Hanselman, J. Rasmussen, and S. Rasmussen.