Constraints on families of smooth 4–manifolds from Bauer–Furuta invariants

Baraglia, David

doi:10.2140/agt.2021.21.317

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Constraints on families of smooth $4$–manifolds from Bauer–Furuta invariants

David Baraglia

Algebraic & Geometric Topology 21 (2021) 317–349

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 $\frac{10}{8}$ theorem. As an application we construct examples of continuous $ℤ_{p}$ –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 $8$ .

Keywords

$4$–manifolds, Seiberg–Witten, Bauer–Furuta

Mathematical Subject Classification 2010

Primary: 57R57

Secondary: 57R22, 57R50

References

Publication

Received: 22 July 2019

Revised: 11 February 2020

Accepted: 8 May 2020

Published: 25 February 2021

Authors

David Baraglia
School of Mathematical Sciences The University of Adelaide Adelaide SA Australia

Volume 21, issue 1 (2021)