Exotic aspherical 4-manifolds

Michael Davis; Kyle Hayden; Jingyin Huang; Daniel Ruberman; Nathan Sunukjian

Exotic aspherical 4-manifolds

From To appear in forthcoming issues by Michael Davis, Kyle Hayden, Jingyin Huang, Daniel Ruberman, Nathan Sunukjian

Abstract

We prove that there exist closed, aspherical smooth 4-manifolds that are homeomorphic but not diffeomorphic. These provide counterexamples to a smooth analog of the Borel conjecture in dimension four.

Keywords

4-manifolds, Borel conjecture, Coxeter groups, aspherical manifolds, exotic smooth structures

Mathematical Subject Classification

Primary 2020: 57R55 Secondary: 20F55

Milestones

Accepted: 2026-02-26

Authors

Michael Davis

Department of Mathematics, Math Tower, The Ohio State University, Columbus, OH 43210

Kyle Hayden

Department of Mathematics & Computer Science, Rutgers University - Newark, Newark, NJ 07102

Jingyin Huang

Department of Mathematics, Math Tower, The Ohio State University, Columbus, OH 43210

Daniel Ruberman

Department of Mathematics, MS 050, Brandeis University, Waltham, MA 02454

Nathan Sunukjian

Department of Mathematics and Statistics, Calvin University, Grand Rapids, MI 49506