Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 61, Number 4 (2009), 1205-1241.
The generalized Lefschetz number of homeomorphisms on punctured disks
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.
J. Math. Soc. Japan Volume 61, Number 4 (2009), 1205-1241.
First available in Project Euclid: 6 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 55M20: Fixed points and coincidences [See also 54H25]
MATSUOKA, Takashi. The generalized Lefschetz number of homeomorphisms on punctured disks. J. Math. Soc. Japan 61 (2009), no. 4, 1205--1241. doi:10.2969/jmsj/06141205. https://projecteuclid.org/euclid.jmsj/1257520505.