Geodesic
Rank inequalities for the Heegaard Floer homology of branched covers
Documenta mathematica, Tome 27 (2022), pp. 581-612.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 57M12, 57R58
Keywords: Heegaard Floer homology, double branched cover 
@article{DOCMA_2022__27__a53,
     author = {Hendricks, Kristen and Lidman, Tye and Lipshitz, Robert},
     title = {Rank inequalities for the {Heegaard} {Floer} homology of branched covers},
     journal = {Documenta mathematica},
     pages = {581--612},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a53/}
}
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Hendricks, Kristen; Lidman, Tye; Lipshitz, Robert. Rank inequalities for the Heegaard Floer homology of branched covers. Documenta mathematica, Tome 27 (2022), pp. 581-612. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a53/