Kristen Pueschel

Ph.D. (2016) Cornell University

First Position

Postdoctoral Associate, University of Arkansas


On Residual Properties of Groups and Dehn Functions for Mapping Tori of Right Angled Artin Groups


Research Area

geometric group theory


Given a group G and an automorphism φ : G → G, the algebraic mapping torus Mφ, is the HNN-extension of G where the stable letter conjugates g to φ(g). In this thesis, we study mapping tori with base groups G that are right angled Artin groups on few generators. In particular, we examine how the Dehn function of a mapping torus depends on the automorphism φ used to generate the group when G is F2 × Z or Z 2 ∗ Z. We then extend our methods to produce bounds for the Dehn functions of other mapping tori with few-generator base groups. A group G is residually finite if for every g ∈ G − {1}, there is a finite quotient of G in which the image of g is non-trivial. The hydra are a family of groups with fast-growing Dehn functions; the Dehn function of each group is equivalent to an Ackermann function. In this thesis we show that hydra are not residually finite, answering a question of Kharlampovich, Myasnikov, and Sapir. A group G is residually solvable if for every g ∈ G−{1}, there is a solvable quotient of G in which the image of g is non-trivial. In this thesis we introduce and explore properties of the function that measures the smallest derived length of a solvable quotient in which g survives, in terms of the length of g.