L-space intervals for graph manifolds and cables

Sarah Rasmussen (Cambridge )

Monday 1st February, 2016 16:00-17:00 Maths 522


For any graph manifold with torus boundary, we compute the interval of Dehn-fillings admitting co-oriented taut foliations, or equivalently in this case, the interval of Dehn-fillings with non-trivial reduced Heegaard Floer homology, i.e., non-L-spaces.  In the case of fiber complements in rational homology sphere graph manifolds, this generalizes a result of Jankins, Neumann, and Naimi.  As a non-graph-manifold application of this result, we compute the L-space interval for any cable of a Floer simple knot complement in a closed three-manifold in terms of the original L-space interval, generalizing a result of Hedden and Hom.

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