Surface homeomorphisms and their lifts by covering maps
Mehdi Yazdi (Oxford)
Monday 27th November, 2017 16:00-17:00 Maths 311B
A generic surface homeomorphism (up to isotopy) is called
pseudo-Anosov. These maps come equipped with an algebraic integer that measures
how much the map stretches/shrinks in different direction, called stretch factor.
Given a surface homeomorsphism, one can ask if it is the lift (by a branched or
unbranched cover) of another homeomorphism on a simpler surface possibly of small genus.
Farb conjectured that if the algebraic degree of the stretch factor is bounded above, then
the map can be obtained by lifting another homeomorphism on a surface of bounded genus.
This was known to be true for quadratic algebraic integers by a Theorem of Franks-Rykken.