MATHEMATICS COLLOQUIUM - Ioana Suvaina (Vanderbilt University)
Abstract: The existence or non-existence of Einstein metrics on a topological
4-space is fundamentally related to the differential structure considered.
We will discuss this property in the context of the geography of four
manifolds. Most of the differential structures considered are non standard.
In the case of the standard smooth structure, where the manifolds are connected
sums of complex projective spaces and complex projective spaces
with the reversed orientation, we exhibit infinitely many non equivalent smooth
actions of finite cyclic groups. We show that these actions give obstructions
to the existence of Einstein metrics.