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.
Publié le : 2009-10-15
Classification:
generalized Lefschetz number,
fixed point,
periodic point,
braid,
Nielsen-Thurston classification theory of homeomorphisms,
punctured disk,
37E30,
55M20
@article{1257520505,
author = {MATSUOKA, Takashi},
title = {The generalized Lefschetz number of homeomorphisms on punctured disks},
journal = {J. Math. Soc. Japan},
volume = {61},
number = {3},
year = {2009},
pages = { 1205-1241},
language = {en},
url = {http://dml.mathdoc.fr/item/1257520505}
}
MATSUOKA, Takashi. The generalized Lefschetz number of homeomorphisms on punctured disks. J. Math. Soc. Japan, Tome 61 (2009) no. 3, pp. 1205-1241. http://gdmltest.u-ga.fr/item/1257520505/