Phd Thesis

A copy of my PhD thesis in the state it has been submitted. This will be updated once complete.

This thesis includes a new construction of groups of type FP that uniquely uses graphical small cancellation theory to control the topology of the relevant objects. We further show that we are able to construct uncountably many quasi-isometry classes of such groups in this way and go on to prove various properties of these groups.

Papers

Click on a title for more information including an abstract and relevant links.

Title	Status
Groups of type FP via graphical small cancellation	Accepted
Abstract We construct an uncountable family of groups of type FP. In contrast to every previous construction of non-finitely presented groups of type FP we do not use Morse theory on cubical complexes; instead we use Gromov’s graphical small cancellation theory.	arx
Uncountably many quasi-isometry classes of groups of type FP	In progress
Some spectacular complexes	In progress