Microbundles (Ex)
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{{beginthm|Exercise|{{citeD|Milnor1964|Lemma 2.1, Theorem 2.2}}}} | {{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 | + | # 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 | + | # Let $M$ be a smooth manifold. Show that $TM$ and $\xi_M$ are isomorphic microbundles. |
{{endthm}} | {{endthm}} | ||
</wikitex> | </wikitex> |
Revision as of 02:29, 28 May 2012
Exercise 0.1 [Milnor1964, Lemma 2.1, Theorem 2.2].
- Let be a topological manifold. Show that is a microbundle.
- Let be a smooth manifold. Show that and are isomorphic microbundles.