Faithful linear representations of the braid groups
Finite presentations for the mapping class group via the ordered complex of curves.
Finite subset spaces of graphs and punctured surfaces.
Fixed points for positive permutation braids
Making use of the Nielsen fixed point theory, we study a conjugacy invariant of braids, which we call the level index function. We present a simple algorithm for computing it for positive permutation cyclic braids.
Free group automorphisms, invariant orderings and topological applications.