Karen Vogtmann

Tethers and Homology stability

The homology of many natural sequences of groups {G_n} is

stable, in the sense that H_i(G_n) is independent of n for n

sufficiently large with respect to i.  This is true for braid groups,

mapping class groups, and automorphism groups of free groups, among

many others.  The standard way of proving homology stability theorems

is to find a highly-connected complex on which the group G_n acts so

that the lower rank groups G_i appear as cell stabilizers,  then to

work with a spectral sequence arising from this action.

    We will explain "tethered" variations of standard complexes which

simplify the proofs of homology stability in several cases, and

establish homology stability in new cases. This is joint work with

Allen Hatcher.