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arXiv · 2512.14183

Notions of simple type for Bauer--Furuta invariants

Tsuyoshi Kato·Daisuke Kishimoto·Nobuhiro Nakamura·Kouichi Yasui
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Abstract

By extending the notion of simple type for the Seiberg--Witten invariant of a 4-manifold, we introduce notions of BF blowup simple type and BF homogeneous type for the Bauer--Furuta invariant and study their applications. Specifically, we show that the existence of an immersed 2-sphere with a certain condition guarantees BF blowup simple type. As an application, we determine the Bauer--Furuta invariant of a 4-manifold obtained by a logarithmic transformation along a torus in a fishtail neighborhood. We also give constraints on gluing decompositions of 4-manifolds by using BF homogeneous type. To prove these results, we also give gluing formulae and an immersed adjunction inequality for Bauer--Furuta invariants.

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Tsuyoshi Kato, Daisuke Kishimoto, Nobuhiro Nakamura, Kouichi Yasui. 2025-12-16. Notions of simple type for Bauer--Furuta invariants. https://arxiv.org/abs/2512.14183

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