Notions of simple type for Bauer--Furuta invariants
Geometric Topology
2025-12-17 v1 Algebraic Topology
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.
Cite
@article{arxiv.2512.14183,
title = {Notions of simple type for Bauer--Furuta invariants},
author = {Tsuyoshi Kato and Daisuke Kishimoto and Nobuhiro Nakamura and Kouichi Yasui},
journal= {arXiv preprint arXiv:2512.14183},
year = {2025}
}
Comments
27 pages, 2 figures