Work

Corks for exotic diffeomorphisms

Year: 2026

Type: article

Abstract: We prove a localization theorem for exotic diffeomorphisms, showing that every diffeomorphism of a compact simply connected 4-manifold that is isotopic to the identity after stabilizing with one copy of S 2 S 2 is smoothly isotopic to a diffeomorphism that is supported on a contractible submanifold.For those that require more than one copy of S 2 S 2 , we prove that the diffeomorphism can be isotoped to one that is supported in a submanifold homotopy equivalent to a wedge of 2-spheres, with null-homotopic inclusion map.We investigate the implications of these results by applying them to known exotic diffeomorphisms.

Source: Geometry & Topology

DOI: 10.2140/gt.2026.30.2297

Authors: Vyacheslav Krushkal, Anubhav Mukherjee, Mark Powell, Terrin Warren

Institutions: University of Virginia, Princeton University, University of Glasgow, California Polytechnic State University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Science Foundation, Engineering and Physical Sciences Research Council

Awards: Topology of 4-Manifolds, Embeddings, and Stable Homotopy Invariants of Links, Geometric Classification Theory and Invariants of 4-Manifolds, Smooth 4-Manifolds: 2-3, 5- and 6-Dimensional Perspectives, Smooth Isotopy, Gauge Theory and Contact Geometry