K-theory of mapping class groups III Odd torsion, by Luke Hodgkin

This is the long-awaited calculation of the odd-torsion in K^*(B Gamma^n) (mapping-class groups for punctured spheres). The size and location of the torsion (it's all in K^1) is completely calculated, together with where it comes from and why; and there is information about the module structure over K^*(BSO(3)). Methods are: (a) the description of B Gamma in terms of function spaces due to Bodigheimer Cohen and Peim and (b) author's earlier calculation of the structure of K^* mod torsion (Math.Z. 218, 611-634). This is my last communication on this subject; if anyone wants to find the 2-torsion, good luck to them.

Address: King's College, Strand, London WC2R 2LS, UK.

Luke Hodgkin <luke.hodgkin@kcl.ac.uk>