Topological 4-manifolds with 4-dimensional fundamental group

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Topological 4-manifolds with 4-dimensional fundamental group. / Kasprowski, Daniel; Land, Markus.

I: Glasgow Mathematical Journal, Bind 64, 2022, s. 454–461.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Kasprowski, D & Land, M 2022, 'Topological 4-manifolds with 4-dimensional fundamental group', Glasgow Mathematical Journal, bind 64, s. 454–461. https://doi.org/10.1017/S0017089521000215

APA

Kasprowski, D., & Land, M. (2022). Topological 4-manifolds with 4-dimensional fundamental group. Glasgow Mathematical Journal, 64, 454–461. https://doi.org/10.1017/S0017089521000215

Vancouver

Kasprowski D, Land M. Topological 4-manifolds with 4-dimensional fundamental group. Glasgow Mathematical Journal. 2022;64:454–461. https://doi.org/10.1017/S0017089521000215

Author

Kasprowski, Daniel ; Land, Markus. / Topological 4-manifolds with 4-dimensional fundamental group. I: Glasgow Mathematical Journal. 2022 ; Bind 64. s. 454–461.

Bibtex

@article{364eecf0cebf40c0a91123cdb9c7bc12,
title = "Topological 4-manifolds with 4-dimensional fundamental group",
abstract = "Let be a group satisfying the Farrell-Jones conjecture and assume that is a 4-dimensional Poincar{\'e} duality space. We consider topological, closed, connected manifolds with fundamental group whose canonical map to has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby-Siebenmann invariant. If is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby-Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel's conjecture, and simply connected manifolds where rigidity is a consequence of Freedman's classification results.",
keywords = "2020 Mathematics Subject Classification, 57K40, 57N65",
author = "Daniel Kasprowski and Markus Land",
note = "Publisher Copyright: {\textcopyright} The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust.",
year = "2022",
doi = "10.1017/S0017089521000215",
language = "English",
volume = "64",
pages = "454–461",
journal = "Glasgow Mathematical Journal",
issn = "0017-0895",
publisher = "Cambridge University Press",

}

RIS

TY - JOUR

T1 - Topological 4-manifolds with 4-dimensional fundamental group

AU - Kasprowski, Daniel

AU - Land, Markus

N1 - Publisher Copyright: © The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust.

PY - 2022

Y1 - 2022

N2 - Let be a group satisfying the Farrell-Jones conjecture and assume that is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group whose canonical map to has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby-Siebenmann invariant. If is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby-Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel's conjecture, and simply connected manifolds where rigidity is a consequence of Freedman's classification results.

AB - Let be a group satisfying the Farrell-Jones conjecture and assume that is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group whose canonical map to has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby-Siebenmann invariant. If is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby-Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel's conjecture, and simply connected manifolds where rigidity is a consequence of Freedman's classification results.

KW - 2020 Mathematics Subject Classification

KW - 57K40

KW - 57N65

UR - http://www.scopus.com/inward/record.url?scp=85111077910&partnerID=8YFLogxK

U2 - 10.1017/S0017089521000215

DO - 10.1017/S0017089521000215

M3 - Journal article

AN - SCOPUS:85111077910

VL - 64

SP - 454

EP - 461

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

ER -

ID: 276857566