Subject: question for the list
From: Jeffrey Herschel Giansiracusa <giansira@maths.ox.ac.uk>
Date: Wed, 10 May 2006 10:54:19 +0100 (BST)

I'm interested in the rational cohomology of the group Gamma of 
automorphisms (over the integers) of the K3 lattice (i.e. two copies 
of the E_8 form plus three copies of the rank 2 hyperbolic form H).

In particular, BGamma includes into BO(3,19) \simeq BO(3)xBO(19), 
and I'd like to know which monomials in the Pontrjagin classes of BO(3)
(or BO(19)) pull back to rationally nonzero classes on BGamma.

Borel's stable range is tiny for this particular arithmetic group, 
so I need something more subtle.

Does anybody have know of any references to this sort of thing?


Jeff Giansiracusa