A remark on taut foliations and Floer homology

2023/09/03 by Francesco Lin, Lin, Francesco · 1 citation
Mathematics · Medicine · Computer Science · #Geometric and Algebraic Topology #Botulinum Toxin and Related Neurological Disorders #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2309.01222

Abstract

It is well-known that the reduced Floer homology of a rational homology sphere admitting a taut foliation does not vanish. We strengthen this by showing that (when thought of as an \mathbbF[U]-module) it also admits a direct \mathbbF-summand. Hence, one could potentially detect counterexamples to the foliation part of the L-space conjecture via purely Floer theoretic computations.

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