26 research outputs found
Mapping tori of small dilatation irreducible train-track maps
We prove that for every P there is a bound B depending only on P so that the
mapping torus of every P--small irreducible train-track map can be obtained by
surgery from one of B mapping tori. We show that given an integer P>0 there is
a bound depending only on P, so that there exists a presentation of the
fundamental group of the mapping torus of a P--small irreducible train-track
map with less than M generators and M relations.Comment: Some figures in colo
On the minimum dilatation of braids on punctured discs
We find the minimum dilatation of pseudo-Anosov braids on n-punctured discs
for 3 <= n <= 8. This covers the results of Song-Ko-Los (n=4) and Ham-Song
(n=5). The proof is elementary, and uses the Lefschetz formula.Comment: 16 pages, LaTeX with amsart style. Mathematica source code included