Doubles of Gluck twists: A five-dimensional approach

David Gabai; Patrick Naylor; Hannah Schwartz

doi:10.1016/j.aim.2025.110455

Doubles of Gluck twists: A five-dimensional approach

David Gabai
, Patrick Naylor
, Hannah Schwartz

Mathematics

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

Abstract

Using a 5-dimensional perspective, we balance algebraic and geometric handle cancellation to show that doubles of Gluck twists of certain 2-spheres embedded in the 4-sphere with two minima are standard. This includes all 2-spheres which are unions of ribbon discs, one of which has undisking number one. As an application, we produce new examples of Schoenflies balls not known to be standard.

Original language	English (US)
Article number	110455
Journal	Advances in Mathematics
Volume	480
DOIs	https://doi.org/10.1016/j.aim.2025.110455
State	Published - Nov 2025

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

4-manifolds
Gluck twists
Low-dimensional topology
Poincaré Conjecture
Schoenflies Conjecture

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10.1016/j.aim.2025.110455

Cite this

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title = "Doubles of Gluck twists: A five-dimensional approach",

abstract = "Using a 5-dimensional perspective, we balance algebraic and geometric handle cancellation to show that doubles of Gluck twists of certain 2-spheres embedded in the 4-sphere with two minima are standard. This includes all 2-spheres which are unions of ribbon discs, one of which has undisking number one. As an application, we produce new examples of Schoenflies balls not known to be standard.",

keywords = "4-manifolds, Gluck twists, Low-dimensional topology, Poincar{\'e} Conjecture, Schoenflies Conjecture",

author = "David Gabai and Patrick Naylor and Hannah Schwartz",

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language = "English (US)",

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AB - Using a 5-dimensional perspective, we balance algebraic and geometric handle cancellation to show that doubles of Gluck twists of certain 2-spheres embedded in the 4-sphere with two minima are standard. This includes all 2-spheres which are unions of ribbon discs, one of which has undisking number one. As an application, we produce new examples of Schoenflies balls not known to be standard.

KW - 4-manifolds

KW - Gluck twists

KW - Low-dimensional topology

KW - Poincaré Conjecture

KW - Schoenflies Conjecture

UR - https://www.scopus.com/pages/publications/105011842173

UR - https://www.scopus.com/pages/publications/105011842173#tab=citedBy

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SN - 0001-8708

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JO - Advances in Mathematics

JF - Advances in Mathematics

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ER -

Doubles of Gluck twists: A five-dimensional approach

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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