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arXiv · 0804.1401

The generalized Lefschetz number of homeomorphisms on punctured disks

Takashi Matsuoka
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Abstract

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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Takashi Matsuoka. 2009-09-19. The generalized Lefschetz number of homeomorphisms on punctured disks. https://arxiv.org/abs/0804.1401

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