Wednesday, June 13th, 2012 | Author: Konrad Voelkel
I want to discuss the elementary basics of Thom spaces of vector bundles. To start, I explain general one-point compactification and a different construction on vector spaces, then I do it for vector bundles to define the Thom space. I also discuss suspension of topological spaces and how adding a trivial vector space (or bundle) corresponds to suspension under the forming of Thom spaces.
Motto: (Thom space:Suspension)::(Vector bundle:Trivial bundle) or
"Thom spaces are twisted suspensions"
Honestly, I really want to talk about algebraic (motivic) Thom spaces some day, but these are some preliminaries to understand what's going on, so I want to get this out first.