On topological blow-up
Taro Yoshino
Consider a Lie group G (or more generally, a topological group) acts continuously on a manifold M (or more generally, a locally compact Hausdorff space). The quotient space X : = G \ M is locally compact, but not always Hausdorff. In this talk, we introduce a method to understand the topology on such a non-Hausdorff space X. More precisely, for a given locally compact (not necessarily Hausdorff) space X, we construct a locally compact Hausdorff space Y, and a map τ : X → 2^Y. Then, the pair (Y,τ) has a complete information on the topology on X. In particular, (Y,τ) describes convergence of sequences or filters on X.