RANK INEqUALITIES FOR THE HEEGAARD FLOER HOMOLOGY OF BRANCHED COVERS

Kristen Hendricks; Tye Lidman; Robert Lipshitz

doi:10.25537/dm.2022v27.581-612

RANK INEqUALITIES FOR THE HEEGAARD FLOER HOMOLOGY OF BRANCHED COVERS

Kristen Hendricks, Tye Lidman, Robert Lipshitz

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that if L is a nullhomologous link in a 3-manifold Y and Σ(Y, L) is a double cover of Y branched along L then for each spinc-structure s on Y there is an inequality dim HF (Σ(Y, L), π∗s; F2) ≥ dim HF (Y, s; F2). 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.

Original language	English (US)
Pages (from-to)	581-612
Number of pages	32
Journal	Documenta Mathematica
Volume	27
DOIs	https://doi.org/10.25537/dm.2022v27.581-612
State	Published - 2022

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

branched covers
Heegaard Floer homology

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10.25537/dm.2022v27.581-612

Cite this

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title = "RANK INEqUALITIES FOR THE HEEGAARD FLOER HOMOLOGY OF BRANCHED COVERS",

abstract = "We show that if L is a nullhomologous link in a 3-manifold Y and Σ(Y, L) is a double cover of Y branched along L then for each spinc-structure s on Y there is an inequality dim HF (Σ(Y, L), π∗s; F2) ≥ dim HF (Y, s; F2). 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.",

keywords = "branched covers, Heegaard Floer homology",

author = "Kristen Hendricks and Tye Lidman and Robert Lipshitz",

note = "Funding Information: We thank Steven Frankel, Tim Large, Yi Ni, Rachel Roberts, and Chuck Weibel for interesting discussions. We thank the referee for further suggestions and corrections. KH was supported by NSF grant DMS-2019396 and a Sloan Research Fellowship. TL was supported by NSF grant DMS-1709702 and a Sloan Research Fellowship. RL was supported by NSF grant DMS-1810893. Publisher Copyright: {\textcopyright} 2022",

year = "2022",

doi = "10.25537/dm.2022v27.581-612",

language = "English (US)",

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pages = "581--612",

journal = "Documenta Mathematica",

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T1 - RANK INEqUALITIES FOR THE HEEGAARD FLOER HOMOLOGY OF BRANCHED COVERS

AU - Hendricks, Kristen

AU - Lidman, Tye

AU - Lipshitz, Robert

N1 - Funding Information: We thank Steven Frankel, Tim Large, Yi Ni, Rachel Roberts, and Chuck Weibel for interesting discussions. We thank the referee for further suggestions and corrections. KH was supported by NSF grant DMS-2019396 and a Sloan Research Fellowship. TL was supported by NSF grant DMS-1709702 and a Sloan Research Fellowship. RL was supported by NSF grant DMS-1810893. Publisher Copyright: © 2022

PY - 2022

Y1 - 2022

N2 - We show that if L is a nullhomologous link in a 3-manifold Y and Σ(Y, L) is a double cover of Y branched along L then for each spinc-structure s on Y there is an inequality dim HF (Σ(Y, L), π∗s; F2) ≥ dim HF (Y, s; F2). 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.

AB - We show that if L is a nullhomologous link in a 3-manifold Y and Σ(Y, L) is a double cover of Y branched along L then for each spinc-structure s on Y there is an inequality dim HF (Σ(Y, L), π∗s; F2) ≥ dim HF (Y, s; F2). 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.

KW - branched covers

KW - Heegaard Floer homology

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JO - Documenta Mathematica

JF - Documenta Mathematica

ER -

RANK INEqUALITIES FOR THE HEEGAARD FLOER HOMOLOGY OF BRANCHED COVERS

Abstract

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