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Counterexamples in 4-manifold topology

Counterexamples in 4-manifold topology
Counterexamples in 4-manifold topology

We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain implications e.g. that h-cobordant manifolds are stably homeomorphic, and we provide examples illustrating the failure of other potential implications. The information is conveniently organised in a flowchart and a table.

4-manifolds, equivalence relations
2308-2151
193-249
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Powell, Mark
4aaeb063-734c-4136-9da8-fb2ade23d744
Ray, Arunima
83cc0cbe-d85d-46f1-90ea-e67bc44386b8
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Powell, Mark
4aaeb063-734c-4136-9da8-fb2ade23d744
Ray, Arunima
83cc0cbe-d85d-46f1-90ea-e67bc44386b8

Kasprowski, Daniel, Powell, Mark and Ray, Arunima (2022) Counterexamples in 4-manifold topology. EMS Surveys in Mathematical Sciences, 9 (1), 193-249. (doi:10.4171/EMSS/56).

Record type: Article

Abstract

We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain implications e.g. that h-cobordant manifolds are stably homeomorphic, and we provide examples illustrating the failure of other potential implications. The information is conveniently organised in a flowchart and a table.

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Accepted/In Press date: 4 October 2022
Published date: 2022
Additional Information: Funding Information: D. K. was supported by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy – GZ 2047/1, Projekt-ID 390685813. M. P. was partially supported by EPSRC New Investigator grant EP/T028335/1 and EPSRC New Horizons grant EP/V04821X/1. Publisher Copyright: © 2023 European Mathematical Society Published by EMS Press.
Keywords: 4-manifolds, equivalence relations

Identifiers

Local EPrints ID: 475452
URI: http://eprints.soton.ac.uk/id/eprint/475452
ISSN: 2308-2151
PURE UUID: c4056c30-4716-4d88-999d-8b525b3e1201
ORCID for Daniel Kasprowski: ORCID iD orcid.org/0000-0001-5926-2206

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Date deposited: 17 Mar 2023 17:51
Last modified: 06 Jun 2024 02:17

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Contributors

Author: Daniel Kasprowski ORCID iD
Author: Mark Powell
Author: Arunima Ray

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