41 research outputs found
Isoperimetric inequalities for the handlebody groups
We show that the mapping class group of a handlebody of genus at least 2 has
a Dehn function of at most exponential growth type.Comment: 21 pages, 1 figur
-cohomology for groups of isometries of Hadamard spaces
We show that a discrete group which admits a non-elementary
isometric action on a Hadamard manifold of bounded negative curvature admits an
isometric action on an -space for some with
.Comment: 26 page
Spotted disk and sphere graphs
The disk graph of a handlebody H of gneus with marked
points on the boundary is the graph whose vertices are isotopy classes of disks
disjoint from the marked points and where two vertices are connected by an edge
of length one if they can be realized disjointly. We show that for m=2 the disk
graph contains quasi-isometrically embedded copies of .
Furthermore, the sphere graph of the doubled handlebody of genus with
two marked points contains for every a quasi-isometrically embedded
copy of .Comment: 26 pages, 1 figur
Generating the spin mapping class group by Dehn twists
Let f be a Z/2Z-spin structureon a closed surface S of genus g>3. We
determine a generating set of the stabilizer of f in the mapping class group of
S consisting of Dehn twists about an explicit collection of 2g+1 curves in S.
If g=3 then we also determine a generating set of the stabilizer of an odd
Z/2Z-spin structure consisting of Dehn twists about a collection of 6 curves.Comment: Final version. A considerable simplification in Section 2. 41 pages,
5 figure