Volume 20, issue 5 (2020)

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Null-homologous exotic surfaces in $4$–manifolds

Neil R Hoffman and Nathan S Sunukjian

Algebraic & Geometric Topology 20 (2020) 2677–2685

We exhibit infinite families of embedded tori in 4–manifolds that are topologically isotopic but smoothly distinct. The interesting thing about these tori is that they are topologically trivial in the sense that each bounds a topologically embedded solid handlebody. This implies that there are stably ribbon surfaces in 4–manifolds that are not ribbon.

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ribbon surface, exotically embedded tori
Mathematical Subject Classification 2010
Primary: 57Q45, 57R40, 57R52, 57R57
Secondary: 57M25
Received: 1 August 2019
Revised: 23 September 2019
Accepted: 16 December 2019
Published: 4 November 2020
Neil R Hoffman
Department of Mathematics
Oklahoma State University
Stillwater, OK
United States
Nathan S Sunukjian
Mathematics and Statistics Department
Calvin University
Grand Rapids, MI
United States