arXiv Open Access 2024

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

Antonio Alfieri Fraser Binns

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Abstrak

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 $\mathbf{F}[U]/U$ 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.

Topik & Kata Kunci

math.GT

Penulis (2)

Antonio Alfieri

Fraser Binns

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APA MLA BibTeX

Alfieri, A., Binns, F. (2024). Is the geography of Heegaard Floer homology restricted or the $L$-space conjecture false?. https://arxiv.org/abs/2404.00490

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓