Open Access
May 2007 A gluing theorem for the relative Bauer-Furuta invariants
Ciprian Manolescu
J. Differential Geom. 76(1): 117-153 (May 2007). DOI: 10.4310/jdg/1180135667


In a previous paper we have constructed an invariant of four-dimensional manifolds with boundary in the form of an element in the stable homotopy group of the Seiberg-Witten Floer spectrum of the boundary. Here we prove that when one glues two four-manifolds along their boundaries, the Bauer-Furuta invariant of the resulting manifold is obtained by applying a natural pairing to the invariants of the pieces. As an application, we show that the connected sum of three copies of the K3 surface contains no exotic nuclei. In the process we also compute the Floer spectrum for several Seifert fibrations.


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Ciprian Manolescu. "A gluing theorem for the relative Bauer-Furuta invariants." J. Differential Geom. 76 (1) 117 - 153, May 2007.


Published: May 2007
First available in Project Euclid: 25 May 2007

zbMATH: 1128.57031
MathSciNet: MR2312050
Digital Object Identifier: 10.4310/jdg/1180135667

Rights: Copyright © 2007 Lehigh University

Vol.76 • No. 1 • May 2007
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