The topology at infinity of real algebraic manifolds

Geometry Topology Seminar
Friday, April 2, 2010 - 14:00
1 hour (actually 50 minutes)
Skiles 269
A noncompact smooth manifold X has a real algebraic structure if and only if X is tame at infinity, i.e. X is the interior of a compact manifold with boundary. Different algebraic structures on X can be detected by the topology of an algebraic compactification with normal crossings at infinity. The resulting filtration of the homology of X is analogous to Deligne's weight filtration for nonsingular complex algebraic varieties.