The generalized Lefschetz number of homeomorphisms on punctured disks

Details The generalized Lefschetz number of homeomorphisms on punctured disks The generalized Lefschetz number of homeomorphisms on punctured disks

2008-04-09

arxiv.org/abs/0804.1401v2

Mathematics

Dynamical Systems

30 pages

Scientific paper

We compute the generalized Lefschetz number of orientation-preserving self-homeomorphisms of a compact punctured disk, using the fact that homotopy classes of these homeomorphisms can be identified with braids. This result is applied to study Nielsen-Thurston canonical homeomorphisms on a punctured disk. We determine, for a certain class of braids, the rotation number of the corresponding canonical homeomorphisms on the outer boundary circle. Also,it is shown that the canonical homeomorphisms corresponding to some braids are pseudo-Anosov.

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