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The Center Of Some Braid Groups And The Farrell Cohomology Of Certain Pure Mapping Class Groups, Craig A. Jensen, Yu Qing Chen, Henry H. Glover
The Center Of Some Braid Groups And The Farrell Cohomology Of Certain Pure Mapping Class Groups, Craig A. Jensen, Yu Qing Chen, Henry H. Glover
Mathematics Faculty Publications
In this paper we first show that many braid groups of low genus surfaces have their centers as direct factors. We then give a description of centralizers and normalizers of prime order elements in pure mapping class groups of surfaces with spherical quotients using automorphism groups of fundamental groups of the quotient surfaces. As an application, we use these to show that the primary part of the Farrell cohomology groups of certain mapping class groups are elementary abelian groups. At the end we compute the primary part of the Farrell cohomology of a few pure mapping class groups.
The Euler Characteristic Of The Whitehead Automorphism Group Of A Free Product, Craig A. Jensen, Jon Mccammond, John Meier
The Euler Characteristic Of The Whitehead Automorphism Group Of A Free Product, Craig A. Jensen, Jon Mccammond, John Meier
Mathematics Faculty Publications
A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups. In particular, we establish formulae for the Euler characteristics of: the group of Whitehead automorphisms...