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# 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

#### 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