Finiteness Properties for Handlebody Mapping Class GroupsCornell University, 1997 - 240 pages |
Common terms and phrases
2-sphere a₁ analogous arc of intersection arc representatives arc segments arc system automorphism boundary circles boundary components C₁ Chapter classes of arcs classes of diffeomorphisms contractible corresponding D-local D₁ defined definition deformation retracts Dehn twists denote diffeomorphism disc representatives disc system discs D1 endpoints essential discs Euler characteristic f(vi f₁ f₁(v fact Figure finite number finitely presented fixes follows genus g given group of isotopy handlebody mapping class Hence homological stability homotopy equivalent identity induction inessential isomorphism isotopy classes isotopy extension Lemma locally finite mapping class group maximal system minimal pair of pants pointwise preserves PROOF OF LEMMA properly embedded punctures quotient restriction result set of arcs set of representatives short exact sequence simple system simplex simplicial map simply connected splitting St(v stably subcomplex subgroup subset surgery surjective system of arcs system of discs Theorem v₁ vertex vertices