Rank inequalities for the Heegaard Floer homology of branched covers
We show that if L is a nullhomologous link in a 3-manifold Y and \Sigma(Y, L) is a double cover of Y branched along L then for each spin ^c -structure \mathfrak{s} on Y there is an inequality \dim\widehat{HF}(\Sigma(Y, L), \pi^\ast\mathfrak{s}; \mathbb{F}_2) \geq \dim \widehat{HF} (Y, \mathfrak{s};...
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| Published in: | Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung. Vol. 27; pp. 581 - 612 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| ISSN: | 1431-0635, 1431-0643 |
| Online Access: | Get full text |
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| Summary: | We show that if L is a nullhomologous link in a 3-manifold Y and \Sigma(Y, L) is a double cover of Y branched along L then for each spin ^c -structure \mathfrak{s} on Y there is an inequality
\dim\widehat{HF}(\Sigma(Y, L), \pi^\ast\mathfrak{s}; \mathbb{F}_2) \geq \dim \widehat{HF} (Y, \mathfrak{s}; \mathbb{F}_2).
We discuss the relationship with the L -space conjecture and give some other topological applications, as well as an analogous result for sutured Floer homology. |
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| ISSN: | 1431-0635 1431-0643 |
| DOI: | 10.4171/dm/878 |