Is the geography of Heegaard Floer homology restricted or the $L$-space conjecture false?
| Autor: | Alfieri, Antonio, Binns, Fraser |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 19 pages |
| Databáze: | arXiv |
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