Journal of the Mathematical Society of Japan

The generalized Lefschetz number of homeomorphisms on punctured disks

Takashi MATSUOKA

Full-text: Open access

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. 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.

Article information

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

Dates
First available in Project Euclid: 6 November 2009

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1257520505

Digital Object Identifier
doi:10.2969/jmsj/06141205

Zentralblatt MATH identifier
05651149

Mathematical Reviews number (MathSciNet)
MR2588509

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

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

Citation

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. http://projecteuclid.org/euclid.jmsj/1257520505.


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