Bauer-Furuta invariants under Z_2-actions

Details Bauer-Furuta invariants under Z_2-actions Bauer-Furuta invariants under Z_2-actions

2007-05-11

arxiv.org/abs/0705.1595v2

Mathematics

Geometric Topology

21 pages, typos corrected, several descriptions changed

Scientific paper

S.Bauer and M.Furuta defined a stable cohomotopy refinement of the Seiberg-Witten invariants. In this paper, we prove a vanishing theorem of Bauer-Furuta invariants for 4-manifolds with smooth Z/2-actions. As an application, we give a constraint on smooth Z/2-actions on homotopy K3#K3, and construct a nonsmoothable locally linear Z/2-action on K3#K3. We also construct a nonsmoothable locally linear Z/2-action on $K3$.

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