Dale Rolfsen

This talk is dedicated to the memory of Bernard Perron, who recently passed away. We collaborated on work involving automorphisms of a free group: he showed me how to understand the induced automorphisms on the lower central series quotients, using...

In joint work with Adam Clay, we establish a necessary condition that an automorphism of an orderable group can preserve an ordering: at least one of its eigenvalues, suitably defined, must be real and positive. Applications will be given to knot...

This will be a mostly expository talk on the new 3-manifold invariant, Heegaard-Floer homology, developed in the last decade in a series of remarkable papers by Ozsvath and Szabo. Emphasis will be on the remarkable applications of the theory.

Abstract: The "group" a knot in 3-space is by definition the fundamental group of its complement; it is one of the oldest algebraic tools used to study knots. Only recently was it discovered that all knot groups can be endowed with a left-invariant...

Algebra and topology are old friends. Many topological problems are solved by applying algebraic methods. But sometimes the relationship can work the other way. My talk will discuss how the topological viewpoint can be used to establish the basic...

Let M be a connected, orientable, piecewise linear manifold of dimension n and let B be a closed submanifold of M. Let PL(M, B) be the group of orientation preserving PL homeomorphisms of M which are pointwise fixed on B. The group operation is...

Classical knot groups, that is fundamental groups of knot complements in 3-space, are known to be torsion-free. However, we show that for many knots, their groups contain generalized torsion: a nontrivial element such that some product of conjugates...

For any non-negative integer n there exist n-cusped hyperbolic 3-manifolds of minimal possible volume. They are sometimes not unique. For example there are exactly two distinct minimal 1-cusped examples: the figure eight complement, and another which...

An ordered group (G,