Entropy of pseudo-Anosovs which fix homology
Presenter
April 15, 2015
Keywords:
- entropy
- Teichmuller theory
- geodesics on Teichmuller space
- entropy minimization
- Linch's inequality
- triangulation of three manifold
- Ellenberg's conjecture
MSC:
- 37D20
- 37Dxx
- 37-xx
- 28D20
- 37A35
- 37Axx
Abstract
We show that the entropy of a pseudo-Anosov which fixes a k-dimensional subspace of homology of a genus g surface is comparable to (k+1)/g. This answers a question of Ellenberg. Key use is made of a recent inequality of Kojima-McShane giving an upper bound on volume in terms of dilatation.