Microbundles (Ex)

Exercise 0.1 [Milnor1964, Theorem 2.2].

1. Let $M$$<wikitex>; {{beginthm|Exercise|{{citeD|Milnor1964|Lemma 2.1, Theorem 2.2}}}} # Let $M$ be a topological manifold. Show that $\xi_M : = (M \times M, M, \Delta_M, p_1)$ is a microbundle. # Let $M$ be a smooth manifold. Show that $TM$ and $\xi_M$ are isomorphic microbundles. {{endthm}} </wikitex> == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises with solution]]M$ be a topological manifold. Show that $\xi_M : = (M \times M, M, \Delta_M, p_1)$$\xi_M : = (M \times M, M, \Delta_M, p_1)$ is a microbundle.

Exercise 0.2 [Milnor1964, Theorem 2.2].

1. Let $M$$M$ be a smooth manifold. Show that $TM$$TM$ and $\xi_M$$\xi_M$ are isomorphic microbundles.