Atlas: Surface dynamics lifted to Abelian covers by Philip Boyland

Atlas home || Conferences | Abstracts | about Atlas

Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

View Abstracts
Conference Homepage

Surface dynamics lifted to Abelian covers
by
Philip Boyland
University of Florida
Coauthors: Gavin Band

Lifting to a covering space is a standard way of unraveling dynamics. We study the lifts of rel pseudoAnosov (pA) maps on surfaces to Abelian covers. Very roughly, the eigenvalues of modulus one of the induced action on homology correspond to a free Abelian cover with a transitive lift of the map and dense leaves of the lifted invariant foliations and those off the unit circle yield semiconjugacies from the lift of the map on the universal Abelian cover to a hyperbolic linear map, or equivalently, they yield transverse, invariant distributions on the surface. We also give conditions for the sharpness of the entropy estimates coming from twisted homology in the covers which correspond to center directions of the action on homology. This is joint work with Gavin Band.

Date received: January 30, 2008