Ribbon homology cobordisms

Aliakbar Daemi; Tye Lidman; David Shea Vela-Vick; C. M.Michael Wong

doi:10.1016/j.aim.2022.108580

Ribbon homology cobordisms

Aliakbar Daemi
, Tye Lidman
, David Shea Vela-Vick
, C. M.Michael Wong

Department of Mathematics

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

13 Scopus citations

Abstract

We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. Using these, we derive obstructions to such cobordisms. As one example of these obstructions, we generalize other recent results on the behavior of knot Floer homology under ribbon concordances. Finally, we provide topological applications, including to Dehn surgery problems.

Original language	English
Article number	108580
Journal	Advances in Mathematics
Volume	408
DOIs	https://doi.org/10.1016/j.aim.2022.108580
State	Published - Oct 29 2022

Keywords

Character varieties
Dehn surgery
Floer homology
Homology cobordism
Ribbon concordance
Thurston geometries

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10.1016/j.aim.2022.108580

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title = "Ribbon homology cobordisms",

abstract = "We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. Using these, we derive obstructions to such cobordisms. As one example of these obstructions, we generalize other recent results on the behavior of knot Floer homology under ribbon concordances. Finally, we provide topological applications, including to Dehn surgery problems.",

keywords = "Character varieties, Dehn surgery, Floer homology, Homology cobordism, Ribbon concordance, Thurston geometries",

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T1 - Ribbon homology cobordisms

AU - Daemi, Aliakbar

AU - Lidman, Tye

AU - Vela-Vick, David Shea

AU - Wong, C. M.Michael

PY - 2022/10/29

Y1 - 2022/10/29

N2 - We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. Using these, we derive obstructions to such cobordisms. As one example of these obstructions, we generalize other recent results on the behavior of knot Floer homology under ribbon concordances. Finally, we provide topological applications, including to Dehn surgery problems.

AB - We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. Using these, we derive obstructions to such cobordisms. As one example of these obstructions, we generalize other recent results on the behavior of knot Floer homology under ribbon concordances. Finally, we provide topological applications, including to Dehn surgery problems.

KW - Character varieties

KW - Dehn surgery

KW - Floer homology

KW - Homology cobordism

KW - Ribbon concordance

KW - Thurston geometries

UR - https://www.scopus.com/pages/publications/85135685527

U2 - 10.1016/j.aim.2022.108580

DO - 10.1016/j.aim.2022.108580

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AN - SCOPUS:85135685527

SN - 0001-8708

VL - 408

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108580

ER -

Ribbon homology cobordisms

Abstract

Keywords

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