Microbundles (Ex)
From Manifold Atlas
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− | {{beginthm|Exercise|{{citeD|Milnor1964| | + | {{beginthm|Exercise|{{citeD|Milnor1964|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 topological manifold. Show that $\xi_M : = (M \times M, M, \Delta_M, p_1)$ is a microbundle. | ||
+ | {{endthm}} | ||
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+ | {{beginthm|Exercise|{{citeD|Milnor1964|Theorem 2.2}}}} | ||
# Let $M$ be a smooth manifold. Show that $TM$ and $\xi_M$ are isomorphic microbundles. | # Let $M$ be a smooth manifold. Show that $TM$ and $\xi_M$ are isomorphic microbundles. | ||
{{endthm}} | {{endthm}} | ||
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</wikitex> | </wikitex> | ||
== References == | == References == | ||
{{#RefList:}} | {{#RefList:}} | ||
[[Category:Exercises]] | [[Category:Exercises]] | ||
− | [[Category:Exercises | + | [[Category:Exercises with solution]] |
Latest revision as of 11:42, 30 May 2012
Exercise 0.1 [Milnor1964, Theorem 2.2].
- Let be a topological manifold. Show that is a microbundle.
Exercise 0.2 [Milnor1964, Theorem 2.2].
- Let be a smooth manifold. Show that and are isomorphic microbundles.