Topological 4-manifolds with 4-dimensional fundamental group
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Topological 4-manifolds with 4-dimensional fundamental group. / Kasprowski, Daniel; Land, Markus.
In: Glasgow Mathematical Journal, Vol. 64, 2022, p. 454–461.Research output: Contribution to journal › Journal article › Research › peer-review
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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