Mathematical Research Letters

Volume 27 (2020)

Number 6

The Dehn twist on a sum of two $K3$ surfaces

Pages: 1767 – 1783

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n6.a8

Authors

P. B. Kronheimer (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

T. S. Mrowka (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

Ruberman gave the first examples of self-diffeomorphisms of four-manifolds that are isotopic to the identity in the topological category but not smoothly so. We give another example of this phenomenon, using the Dehn twist along a $3$-sphere in the connected sum of two $K3$ surfaces.

The work of the first-named author was supported by the National Science Foundation through NSF grant DMS-1707924.

The work of the second-named author was supported by the National Science Foundation through NSF grant DMS-1808794.

Received 30 January 2020

Accepted 7 April 2020

Published 17 February 2021