MIT Topology Seminar
Monday, February 13, 2006
Room 2-142, 4:30pm
Eric Rains will speak on:
The cohomology ring of the real locus of ${\bar M}_{0,n}$
Abstract: The moduli space $M_{0,n}$ (the set of equivalence classes of
n-tuples of distinct points on the projective line under simultaneous
linear fractional transformations) has a natural compactification to a
smooth projective shceme ${\bar M}_{0,n}$. Since this scheme is defined
over $\Z$, its real locus is a smooth (in general nonorientable)
manifold. The rational cohomology algebra of this manifold has a number
of interesting properties, most notably the fact that its Poincar\'e
polynomial factors completely (in sharp contrast to the corresponding
complex manifold). I'll discuss recent work with Etingof, Henriques,
and Kamnitzer deriving this Poincar\'e polynomial, as well as an
explicit presentation and basis of the cohomology algebra.