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A
gluing formula for families Seiberg–Witten invariants
David Baraglia and Hokuto Konno |
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Geometry & Topology 24 (2020) 1381–1456
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Abstract |
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We prove a gluing formula for the families Seiberg–Witten invariants of families of –manifolds obtained by fibrewise connected sum. Our formula expresses the families Seiberg–Witten invariants of such a connected sum family in terms of the ordinary Seiberg–Witten invariants of one of the summands, under certain assumptions on the families. We construct some variants of the families Seiberg–Witten invariants and prove the gluing formula also for these variants. One variant incorporates a twist of the families moduli space using the charge conjugation symmetry of the Seiberg–Witten equations. The other variant is an equivariant Seiberg–Witten invariant of smooth group actions. We consider several applications of the gluing formula, including obstructions to smooth isotopy of diffeomorphisms, computation of the mod Seiberg–Witten invariants of spin structures, and relations between mod Seiberg–Witten invariants of –manifolds and obstructions to the existence of invariant metrics of positive scalar curvature for smooth group actions on –manifolds. |
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Keywords
Seiberg–Witten, $4$–manifolds, gauge theory, group actions,
diffeomorphisms
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Mathematical Subject Classification 2010
Primary: 57R57
Secondary: 57M60, 57R22
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References |
Publication
Received: 16 January 2019
Revised: 3 August 2019
Accepted: 11 September 2019
Published: 30 September 2020
Proposed: Ciprian Manolescu
Seconded: Simon Donaldson, Yasha Eliashberg
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Authors |
| David Baraglia | |
| School of Mathematical
Sciences The University of Adelaide Adelaide SA Australia |
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| Hokuto Konno | |
| Graduate School of Mathematical
Sciences The University of Tokyo Meguro Tokyo Japan |
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