L-space slopes and bordered Heegaard Floer homology

L-space slopes and bordered Heegaard Floer homology

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Jonathan Hanselman, Columbia University
Fine Hall 314

It is conjectured that for irreducible 3-manifolds, being a non-L-space is equivalent both to having left-orderable fundamental group and to admitting a taut foliation. The latter two properties can be understood in some cases through cut and paste arguments, using a notion of detected slopes for 3-manifolds with toroidal boundary; we seek a similar understanding for L-spaces. For sufficiently nice 3-manifolds with torus boundary, I will describe how L-space slopes can be detected via bordered Heegaard Floer invariants, and I will determine when gluing two such manifolds produces an L-space. Our results, paired with work of Boyer and Clay, imply that the left-orderable/taut foliation/non L-space conjecture is true for graph manifolds with a single JSJ torus. This is joint work with Liam Watson.