Quotient and blow-up of automorphisms of graphs of groups

2015/12/02 by Kaidi Ye, Ye, Kaidi
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1512.00542

arxiv created 2018/01/20 · arxiv updated 2018/01/23

Abstract

In this paper we study the quotient and "blow-up" of graph-of-groups \calG and of their automorphisms H: \calG → \calG. We show that the existence of such a "blow-up" of H: \calG → \calG relative to a given family of "local" graph-of-groups isomorphisms H_i: \calG_i → \calG_i depends crucially on the H_i-conjugacy class of the correction term δ(E_i) for any edge E_i of \calG, where H-congjugacy is a new but natural concept introduced here. As an application we obtain a criterion as to whether a partial Dehn twist can be blown up relative to local Dehn twists to give an actual Dehn twist.

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