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arXiv · 2510.14201

A general connected sum formula for the families Bauer-Furuta invariant

Joshua Tomlin
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Abstract

The Bauer-Furuta invariant of a family of smooth 4-manifolds is a stable cohomotopy refinement of the families Seiberg-Witten invariant and is constructed from a finite dimensional approximation of the Seiberg-Witten monopole map. We prove a general formula for the families Bauer-Furuta invariant of a fibrewise connected sum, extending Bauer's non-parameterised formula. In a subsequent paper, we will use this formula to derive a general connected sum formula for the families Seiberg-Witten invariant which incorporates both the families blow-up formula of Liu and the gluing formula of Baraglia-Konno.

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Joshua Tomlin. 2025-10-16. A general connected sum formula for the families Bauer-Furuta invariant. https://arxiv.org/abs/2510.14201

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