#### Volume 19, issue 3 (2015)

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A new gauge slice for the relative Bauer–Furuta invariants

### Tirasan Khandhawit

Geometry & Topology 19 (2015) 1631–1655
##### Abstract

In this paper, we study Manolescu’s construction of the relative Bauer–Furuta invariants arising from the Seiberg–Witten equations on $4$–manifolds with boundary. The main goal of this paper is to introduce a new gauge fixing condition in order to apply the finite-dimensional approximation technique. We also hope to provide a framework to extend Manolescu’s construction to general $4$–manifolds.

##### Keywords
$4$–manifolds, Seiberg–Witten equations, Bauer–Furuta invariant
Primary: 57R57
Secondary: 57R58
##### Publication
Received: 19 February 2014
Revised: 29 August 2014
Accepted: 30 September 2014
Published: 21 May 2015
Proposed: Ronald Stern
Seconded: Ciprian Manolescu, Simon Donaldson
##### Authors
 Tirasan Khandhawit Kavli Institute for the Physics and Mathematics of the Universe (WPI) UTIAS, The University of Tokyo 5-1-5 Kashiwa-No-Ha, Kashiwa, Chiba 277-8583 Japan