# Mapping class groups of exotic tori and actions by SL(d,Z)

with M. Bustamante, M. Krannich, A. Kupers

### Trans. Amer. Math. Soc., to appear

For an exotic torus, there is a natural homomorphism from the mapping class group to SL(d,Z) given by the action on the fundamental group. We determine when this homomorphism is a split surjection. As part of the proof we compute the mapping class group for all exotic tori obtained from the standard torus by connected sum with an exotic sphere. As an application we give examples of exotic tori that do not admit any nontrivial smooth action by SL(d,Z).