Abstract
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 \({\mathbb{Z}_2}\) -actions. As an application, we give a constraint on smooth \({\mathbb{Z}_2}\) -actions on homotopy K3#K3, and construct a nonsmoothable locally linear \({\mathbb{Z}_2}\) -action on K3#K3. We also construct a nonsmoothable locally linear \({\mathbb{Z}_2}\) -action on K3.
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Nakamura, N. Bauer–Furuta invariants under \({\mathbb{Z}_2}\) -actions. Math. Z. 262, 219–233 (2009). https://doi.org/10.1007/s00209-008-0370-1
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DOI: https://doi.org/10.1007/s00209-008-0370-1