Volume 22, issue 4 (2018)

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Unfolded Seiberg–Witten Floer spectra, I: Definition and invariance

Tirasan Khandhawit, Jianfeng Lin and Hirofumi Sasahira

Geometry & Topology 22 (2018) 2027–2114
Abstract

Let $Y$ be a closed and oriented $3$–manifold. We define different versions of unfolded Seiberg–Witten Floer spectra for $Y$. These invariants generalize Manolescu’s Seiberg–Witten Floer spectrum for rational homology $3$–spheres. We also compute some examples when $Y$ is a Seifert space.

Keywords
3-manifolds, Floer homotopy, Seiberg–Witten theory, Conley index
Primary: 57R57
Secondary: 57R58
Publication
Received: 20 May 2016
Revised: 18 June 2017
Accepted: 22 July 2017
Published: 5 April 2018
Proposed: András I Stipsicz
Seconded: Ciprian Manolescu, Peter Ozsváth
Authors
 Tirasan Khandhawit Kavli IPMU The University of Tokyo Kashiwa Japan Jianfeng Lin Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States Hirofumi Sasahira Faculty of Mathematics Kyushu University Fukuoka Japan