Title: K-theory of mapping class groups III: Odd torsion
Author: Luke Hodgkin
Address: King's College, Strand, London WC2R 2LS, UK.
Email: luke.hodgkin@kcl.ac.uk

This is the long-awaited calculation of the odd-torsion in K^\ast(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^\ast(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^\ast 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.