6533b871fe1ef96bd12d108a
RESEARCH PRODUCT
On the classification of mapping class actions on Thurston's asymmetric metric
Athanase PapadopoulosLixin LiuGuillaume ThéretWeixu Susubject
[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Teichmüller spacePure mathematicsMathematics::Dynamical SystemsGeneral MathematicsProduct metric01 natural sciencesIntrinsic metricMathematics - Geometric Topology[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics32G15 ; 30F60 ; 57M50 ; 57N05Teichmüller spaceMathematics::Complex VariablesInjective metric space010102 general mathematicsMathematical analysisThurston's asymmetric metricGeometric Topology (math.GT)mapping class groupSurface (topology)Mathematics::Geometric TopologyMapping class groupConvex metric spaceMetric (mathematics)010307 mathematical physicsMathematics::Differential Geometrydescription
AbstractWe study the action of the elements of the mapping class group of a surface of finite type on the Teichmüller space of that surface equipped with Thurston's asymmetric metric. We classify such actions as elliptic, parabolic, hyperbolic and pseudo-hyperbolic, depending on whether the translation distance of such an element is zero or positive and whether the value of this translation distance is attained or not, and we relate these four types to Thurston's classification of mapping class elements. The study is parallel to the one made by Bers in the setting of Teichmüller space equipped with Teichmüller's metric, and to the one made by Daskalopoulos and Wentworth in the setting of Teichmüller space equipped with the Weil–Petersson metric.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-10-17 |