Is the geography of Heegaard Floer homology restricted or the L-space conjecture false?

2024/03/30 by Antonio Alfieri, Alfieri, Antonio, Fraser Binns +1
Computer Science · Mathematics · #57K31 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2404.00490

openalex publication_date 2024/03/30 · openalex created_date 2024/04/04 · openalex updated_date 2026/07/28

Abstract

In a recent note F. Lin showed that if a rational homology sphere Y admits a taut foliation then the Heegaard Floer module HF^-(Y) contains a copy of F[U]/U as a summand (arXiv:2309.01222). This implies that either the L-space conjecture is false or that Heegaard Floer homology satisfies a geography restriction. We verify that Lin's geography restriction holds for a wide class of rational homology spheres. Indeed, we show that the Heegaard Floer module HF^-(Y) may satisfy a stronger geography restriction.

Related

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• A remark on the geography problem in Heegaard Floer homology
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