Thom spaces (Ex)
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Diarmuid Crowley (Talk | contribs)
(Created page with "<wikitex>; {{beginthm|Exercise}} Let $X,X_1,X_2$ be $CW$-complexes and let $\xi,\xi_1,\xi_2$ be vector bundles over $X,X_1,X_2$ respectively. Denote by $\xi_1\times\xi_2$ th...")
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(Created page with "<wikitex>; {{beginthm|Exercise}} Let $X,X_1,X_2$ be $CW$-complexes and let $\xi,\xi_1,\xi_2$ be vector bundles over $X,X_1,X_2$ respectively. Denote by $\xi_1\times\xi_2$ th...")
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Revision as of 00:31, 27 March 2012
Exercise 0.1. Let be -complexes and let be vector bundles over respectively. Denote by the product bundle over . Find homeomorphisms
Exercise 0.2. Let be the universal oriented vector bundle of rank and let : be a bundle map.
Exercise 0.3. Define
Show that for all we have . Define
and
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,...?