Notions of simple type for Bauer--Furuta invariants
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908714570612736 |
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| author | Kato, Tsuyoshi Kishimoto, Daisuke Nakamura, Nobuhiro Yasui, Kouichi |
| author_facet | Kato, Tsuyoshi Kishimoto, Daisuke Nakamura, Nobuhiro Yasui, Kouichi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notions of simple type for Bauer--Furuta invariants Kato, Tsuyoshi Kishimoto, Daisuke Nakamura, Nobuhiro Yasui, Kouichi Geometric Topology Algebraic Topology Primary 57K41, Secondary 55Q55 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. |
| title | Notions of simple type for Bauer--Furuta invariants |
| topic | Geometric Topology Algebraic Topology Primary 57K41, Secondary 55Q55 |
| url | https://arxiv.org/abs/2512.14183 |