A survey of group actions on 4-manifolds

Abstract

Over 50 years of work on group actions on $4$-manifolds, from the 1960's to the present, from knotted fixed point sets to Seiberg-Witten invariants, is surveyed. Locally linear actions are emphasized, but differentiable and purely topological actions are also discussed. The presentation is organized around some of the fundamental general questions that have driven the subject of compact transformation groups over the years and their interpretations in the case of $4$-manifolds. Many open problems are formulated. Updates to previous problems sets are given. A substantial bibliography is included.

Added references and citations

References in corpus (8)

• Symmetric symplectic homotopy K3 surfaces
• Isovariant mappings of degree 1 and the Gap Hypothesis
• Group actions on 4-manifolds: some recent results and open questions
• Pseudofree Z/3-actions on K3 surfaces
• Symmetry groups of non-simply-connected four-manifolds
• Free involutions on S^1xS^n
• Rigidity of periodic diffeomorphisms on homotopy K3 surfaces
• On finite simple and nonsolvable groups acting on closed 4-manifolds

Cited by in corpus (4)

• Group actions on 4-manifolds: some recent results and open questions
• Cyclic actions on rational ruled symplectic four-manifolds
• On finite groups acting on homology 4-spheres and finite subgroups of SO(5)
• Simply connected Alexandrov 4-manifolds with positive or nonnegative curvature and torus actions