826 research outputs found
Index realization for automorphisms of free groups
For any surface of genus and (essentially) any collection
of positive integers with Masur and Smillie have shown that there exists a pseudo-Anosov
homeomorphism with precisely singularities in its stable foliation , such that has
precisely separatrices raying out from each .
In this paper we prove the analogue of this result for automorphisms of a
free group , where "pseudo-Anosov homeomorphism" is replaced by "fully
irreducible automorphism" and the Gauss-Bonnet equality is replaced by the index inequality from
Gaboriau, Jaeger, Levitt and Lustig.Comment: 19 pages, 3 figures, 1 table, revised version for publicatio
Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space
We quantitatively relate the Patterson-Sullivant currents and generic
stretching factors for free group automorphisms to the asymmetric Lipschitz
metric on Outer space and to Guirardel's intersection number.Comment: some minor updates and revisions; 18 pages, no figures; to appear in
the Pacific Journal of Mathematic
High distance Heegaard splittings via fat train tracks
We define "fat" train tracks and use them to give a combinatorial criterion
for the Hempel distance of Heegaard splittings for closed orientable
3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on
knots in the three sphere.Comment: 25 pages no figures. to appear in Proceedings of "Knots Groups and
3-manifolds" Marseilles France 200
Perron-Frobenius theory and frequency convergence for reducible substitutions
We prove a general version of the classical Perron-Frobenius convergence
property for reducible matrices. We then apply this result to reducible
substitutions and use it to produce limit frequencies for factors and hence
invariant measures on the associated subshift. The analogous results are well
known for primitive substitutions and have found many applications, but for
reducible substitutions the tools provided here were so far missing from the
theory.Comment: v.2 Minor revisions for submissio
- …