Topological 4-manifolds with 4-dimensional fundamental group
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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.
Original language | English |
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Journal | Glasgow Mathematical Journal |
Volume | 64 |
Pages (from-to) | 454–461 |
ISSN | 0017-0895 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust.
- 2020 Mathematics Subject Classification, 57K40, 57N65
Research areas
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