6533b7defe1ef96bd1275d42
RESEARCH PRODUCT
Presentations for the punctured mapping class groups in terms of Artin groups
Catherine LabruèreLuis Parissubject
Pointwise20F38Class (set theory)presentationsGroup (mathematics)20F36Boundary (topology)Geometric Topology (math.GT)mapping class groupsSurface (topology)Mathematics::Geometric TopologyMapping class groupCombinatoricsMathematics - Geometric TopologyArtin groupsGenus (mathematics)FOS: MathematicsIsotopyGeometry and Topology57N0557N05 20F36 20F38Mathematicsdescription
Consider an oriented compact surface F of positive genus, possibly with boundary, and a finite set P of punctures in the interior of F, and define the punctured mapping class group of F relatively to P to be the group of isotopy classes of orientation-preserving homeomorphisms h: F-->F which pointwise fix the boundary of F and such that h(P) = P. In this paper, we calculate presentations for all punctured mapping class groups. More precisely, we show that these groups are isomorphic with quotients of Artin groups by some relations involving fundamental elements of parabolic subgroups.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1999-11-10 | Algebraic & Geometric Topology |