Journal of the Mathematical Society of Japan

The generalized Lefschetz number of homeomorphisms on punctured disks


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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. As a consequence of this result on the rotation number, it is shown that the canonical homeomorphisms corresponding to some braids are pseudo-Anosov with associated foliations having no interior singularities.

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J. Math. Soc. Japan Volume 61, Number 4 (2009), 1205-1241.

First available: 6 November 2009

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Mathematical Reviews number (MathSciNet)

Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 55M20: Fixed points and coincidences [See also 54H25]

generalized Lefschetz number fixed point periodic point braid Nielsen-Thurston classification theory of homeomorphisms punctured disk


MATSUOKA, Takashi. The generalized Lefschetz number of homeomorphisms on punctured disks. Journal of the Mathematical Society of Japan 61 (2009), no. 4, 1205--1241. doi:10.2969/jmsj/06141205.

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