# 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 == |

## 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.