Schur cohomology and a Kontsevich-Witten genus
Jack Morava
AMS Classification: Primary 14H10, Secondary 55N35, 81R10
Johns Hopkins University: jack@math.jhu.edu
ABSTRACT:
Two-dimensional topological gravity is a kind of physicist's
interpretation of the rational cohomology of the group completion
of the monoid of Riemann surfaces under glueing. It has a
natural algebra of operations, which look vaguely like the
operations in complex cobordism, and Witten has raised the
question of their possible homotopy-theoretic interpretation.
Over the integers this theory turns out to have an interesting
model, which looks a lot like (a double of) the cohomology of
Sp/U. There is an associated formal-group-like object, which
looks unfamiliar because its coordinate seems to be centered at
infinity, corresponding to asymptotic expansions of interest in
physics.
[This paper is a kind of sequel to 'Generalized quantum cohomology'
posted previously on {\bf Hopf}, which has since appeared [in
Contemporary Math. 202, Proceedings of the operads renaissance
conference, ed. Loday, Stasheff, & Voronov]
[ Jack tells me that this is the final version. I've labeled the
DVI file as Schur2-final.dvi and reclused the original version, CWW
7/13/98]