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L-space fillings and generalized solid tori

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arxiv 1603.05016 v1 pith:XO7FYCRY submitted 2016-03-16 math.GT

Thomas J. Gillespie This is my paper · ORCID
classification math.GT
keywords rasmussenl-spacefillingstopologicalworkaskedbeenbuilding
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abstract

Much work has been done recently towards trying to understand the topological significance of being an L-space. Building on work of Rasmussen and Rasmussen, we give a topological characterisation of Floer simple manifolds such that all non-longitudinal fillings are L-spaces. We use this to partially classify L-space twisted torus knots in $S^1 \times S^2$ and resolve a question asked by Rasmussen and Rasmussen.

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  1. Detecting Heegaard Floer homology solid tori

    math.GT 2025-05 accept novelty 7.0 of 10

    A rational homology solid torus is a Heegaard Floer homology solid torus if and only if the Dehn filling along its rational longitude contains a non-separating 2-sphere.

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