Thom spaces (Ex)
Exercise 0.1. Let be -complexes and let be vector bundles over respectively. Denote by the product bundle over . Find homeomorphisms
With the following exercises we work out the details of [Lück2001, page 58f].
Exercise 0.2. Let be the universal oriented vector bundle of rank and let : be a bundle map. Define
Show that for all we have .
Exercise 0.3. Define
where : is the suspension homomorphism. Show that for all we have .
Question 0.4. Can we do similar things for unoriented manifolds, manifolds with spin structure,...?