Braids, Conformal Module and Entropy
Algebraic Geometry
2012-11-26 v2 Complex Variables
Dynamical Systems
Geometric Topology
Abstract
The conformal module of conjugacy classes of braids implicitly appeared in a paper of Lin and Gorin in connection with their interest in the 13. Hilbert Problem. This invariant is the supremum of conformal modules (in the sense of Ahlfors) of certain annuli related to the conjugacy class. This note states that the conformal module is inverse proportional to a popular dynamical braid invariant, the entropy. The entropy appeared in connection with Thurston's theory of surface homeomorphisms. An application of the concept of conformal module to algebraic geometry is given.
Cite
@article{arxiv.1208.1405,
title = {Braids, Conformal Module and Entropy},
author = {Burglind Jöricke},
journal= {arXiv preprint arXiv:1208.1405},
year = {2012}
}
Comments
Research announcement, 4 pages Minor revision, misprints corrected