Mutant knots are notoriously hard to distinguish. Many, but not all, knot invariants take the same value on mutant pairs. Khovanov homology with coefficients in Z/2Z is known to be mutation-invariant, while the bigraded knot Floer homology groups can distinguish mutants such as the famous Kinoshita-Terasaka and Conway pair. However, Baldwin and Levine conjectured that…

During the last thirty years, several (families of) functionals have been defined which model self-avoidance: their values tend to infinity if an embedded object degenerates, e.g., if a sequence of closed simple curves converges to a curve with a self-intersection. Many of these functionals exhibit regularizing effects: they not only ensure embeddedness but in fact…

Let G denote a finite group and X a CW-complex. A homotopy group action is defined as a homotopy class of maps BG -- BAut(X). In this talk we will analyze these actions using techniques from group cohomology. We will show how they relate to geometric actions and how they can be used to construct…