The aim of this paper is to try to extend to monoids some results and ideas in
lowdimensional homotopy theory and combinatorial group theory. In this introduction we …

We give a unified solution to the conjugacy problem for Thompson's groups F,\, TF, T, and V
V. The solution uses “strand diagrams”, which are similar in spirit to braids and generalize …

We give a geometric slice-like characterization for the vanishing of Milnor's link invariants by
proving the k-slice conjecture. This conjecture states that a link L has vanishing Milnor μ ̄ …

In this paper we generalize the setting and results of [1] to higher dimensions. The main
results are Theorem 2 (invariance of Dehn functions under quasi-retractions in the sense of …

We show that diagram groups can be viewed as fundamental groups of spaces of positive
paths on directed 2-complexes (these spaces of paths turn out to be classifying spaces) …

It is proven that every positive one-relator group which satisfies the \rmC'(1\over6) condition
has a finite index subgroup which splits as a free product of two free groups amalgamating a …

The concept of asphericity for relative group presentations was introduced twenty five years
ago. Since then, the subject has advanced and detailed asphericity classifications have …

The Spelling Theorem of BB Newman states that for a one-relator group (a1,…| Wn), any
nontrivial word which represents the identity must contain a (cyclic) subword of W±n longer …

First order Dehn functions of groups (and to a lesser extent monoids) have been the subject
of a considerable amount of study over the last decade. Let us review the definition of these …

This manuscript represents the author's PhD dissertation thesis. The first part studies
decision problems in Thompson's groups F, T, V and some generalizations. The …