#### Volume 17, issue 3 (2017)

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Equivariant corks

### Dave Auckly, Hee Jung Kim, Paul Melvin and Daniel Ruberman

Algebraic & Geometric Topology 17 (2017) 1771–1783
##### Abstract

For any finite subgroup $G$ of $SO\left(4\right)$, we construct a contractible $4$–manifold $C$, with an effective $G$–action on its boundary, that can be embedded in a closed $4$–manifold so that cutting $C$ out and regluing using distinct elements of $G$ will always yield distinct smooth $4$–manifolds.

##### Keywords
corks, smooth structures on 4-manifolds
Primary: 57M99
Secondary: 57R55
##### Publication
Received: 20 April 2016
Revised: 14 September 2016
Accepted: 22 September 2016
Published: 17 July 2017
##### Authors
 Dave Auckly Department of Mathematics Kansas State University Manhattan, KS 66506 United States http://www.math.ksu.edu/~dav/ Hee Jung Kim Department of Mathematical Sciences Seoul National University Seoul 151-747 South Korea http://www.math.uga.edu/directory/hee-jung-kim Paul Melvin Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010 United States http://www.brynmawr.edu/math/people/melvin/ Daniel Ruberman Department of Mathematics Brandeis University MS 050 Waltham, MA 02454 United States http://people.brandeis.edu/~ruberman/