Double point surgery and configurations of surfaces

Abstract

We introduce a new operation, double point surgery, on immersed surfaces in a 4-manifold, and use it to construct knotted configurations of surfaces in many 4-manifolds. Taking branched covers, we produce smoothly exotic actions of Z/m x Z/n on simply connected 4-manifolds with complicated fixed-point sets.

Final version; to appear in Journal of Topology. Removed assertion about the restriction of the Z/m x Z/n action to the Z/m and Z/n subgroups

Cited by in corpus (2)

• Knotted surfaces in 4-manifolds and stabilizations
• $G$-minimality and invariant negative spheres in $G$-Hirzebruch surfaces