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Journal of the London Mathematical Society 1994 49(3):594-613; doi:10.1112/jlms/49.3.594
© 1994 by London Mathematical Society
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© The London Mathematical Society

On the K-Theory of Small Mapping Class Groups

Luke Hodgkin

Mathematics Department, King's College London WC2R 2LS

Received 15 April 1992.

The computations of cohomology for (classifying spaces of) some low genus mapping class groups in Benson and Cohen's recent American Mathematical Society Memoir are applied, via the Atiyah-Hirzebruch spectral sequence, to find the K-theory. It is found that for the three groups in question (4- and 6-punctured spheres and surface of genus 2) the reduced K-theory is profinite, being a direct sum of p-adic groups. There is a non-trivial K1 which cannot arise from representations; the part of K0 which arises via the symmetric group is identified, but in every case there is more, which raises the question of how other representations such as those defined by V. Jones might contribute.


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