Automorphisms of the procongruence pants complex

Abstract

We show that every automorphism of the congruence completion of the extended mapping class group that preserves the set of conjugacy classes of procyclic groups generated by Dehn twists is inner, and that its automorphism group is naturally isomorphic to the automorphism group of the procongruence pants complex. In the genus-zero case, we prove the stronger result that all automorphisms of the profinite completion of the extended mapping class group are inner.

40 pages