Abstract
We show that for every odd prime p, the hyperelliptic mapping class group Δ g has p-periodic cohomology and we determine the p-period. We also compute the Yagita invariant at the prime 2 for even genus, with partial results for odd genus. Finally, we compute the p-part of the Farrell cohomology of Δ g for g=( p−1)/2 and g= p−1, which are the first two cases of Δ g containing p-torsion. Our methods include an analysis of fixed point data and the development of a braid calculus for Δ g .
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