### Research Focus

Topology, geometric (combinatorial) group theory

I am a geometric topologist and a combinatorial group theorist. Much of my work has dealt with the introduction of combinatorial and algebraic themes into geometric problems or geometric themes into combinatorial and algebraic problems. Over the years this work has involved the intermingling of topological manifolds, combinatorial topology, the foundations of piecewise linear topology, simple-homotopy theory, automorphisms of free groups, spaces of length functions on groups and equations over groups. Currently the second best description of me is as a geometric group theorist.

The title I most covet is that of teacher. The writing of a research paper and the teaching of freshman calculus, and everything in between, falls under this rubric. Happy is the person who comes to understand something and then gets to explain it.

In addition to research and teaching I deeply enjoy my role as faculty advisor to undergraduates. These days research, teaching and advising are done in my position as Visiting Professor at Morgan State University, The Urban University of Maryland and one of the classic HBCU's (Historically Black Colleges and Universities).

### Publications

Simplicial structures and transverse cellularity, Annals of Math. (2) 85 (1967), 218–245.

A Course in Simple-homotopy Theory, Graduate Texts in Mathematics 10, Springer Verlag, 1973.

On the dynamics and the fixed subgroup of a free group automorphism (with Martin Lustig), Inv. Math. 96 (1989), 613–638.

Very small group actions on R-trees and Dehn twist automorphisms (with Martin Lustig), Topology 34 (1995), 575–617.

The surjectivity problem for one-generator, one-relator extensions of torsion-free groups (with Colin Rourke), Geometry and Topology 5 (2001), 127–142.

Ode to geometric group theory, American Mathematical Monthly (Aug/Sept 2005), to appear.