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2021 Constraints on families of smooth $4$–manifolds from Bauer–Furuta invariants
David Baraglia
Algebr. Geom. Topol. 21(1): 317-349 (2021). DOI: 10.2140/agt.2021.21.317

Abstract

We obtain constraints on the topology of families of smooth 4–manifolds arising from a finite-dimensional approximation of the families Seiberg–Witten monopole map. Amongst other results these constraints include a families generalisation of Donaldson’s diagonalisation theorem and Furuta’s 108 theorem. As an application we construct examples of continuous p–actions, for any odd prime p, which cannot be realised smoothly. As a second application we show that the inclusion of the group of diffeomorphisms into the group of homeomorphisms is not a weak homotopy equivalence for any compact, smooth, simply connected, indefinite 4–manifold with signature of absolute value greater than 8.

Citation

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David Baraglia. "Constraints on families of smooth $4$–manifolds from Bauer–Furuta invariants." Algebr. Geom. Topol. 21 (1) 317 - 349, 2021. https://doi.org/10.2140/agt.2021.21.317

Information

Received: 22 July 2019; Revised: 11 February 2020; Accepted: 8 May 2020; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.2140/agt.2021.21.317

Subjects:
Primary: 57R57
Secondary: 57R22, 57R50

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 1 • 2021
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