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We compute the generalized Lefschetz number of orientation-preservingself-homeomorphisms of a compact punctured disk, using the fact that homotopyclasses of these homeomorphisms can be identified with braids. This result isapplied to study Nielsen-Thurston canonical homeomorphisms on a punctured disk.We determine, for a certain class of braids, the rotation number of thecorresponding canonical homeomorphisms on the outer boundary circle. Also,it isshown that the canonical homeomorphisms corresponding to some braids arepseudo-Anosov.

The generalized Lefschetz number of homeomorphisms on punctured disks