Normal bundles in products of spheres (Ex)
From Manifold Atlas
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# For all $k$, find an immersion representing the diagonal homology class $(1, 1) \in H_k(S^k \times S^k)$ with trivial normal bundle. | # For all $k$, find an immersion representing the diagonal homology class $(1, 1) \in H_k(S^k \times S^k)$ with trivial normal bundle. | ||
{{endthm}} | {{endthm}} | ||
+ | {{beginrem|Hint}} | ||
+ | You may wish to look at [[Immersing n-spheres in 2n-space (Ex)]] for part 2. | ||
+ | {{endrem}} | ||
</wikitex> | </wikitex> | ||
== References == | == References == | ||
{{#RefList:}} | {{#RefList:}} | ||
[[Category:Exercises]] | [[Category:Exercises]] | ||
− | [[Category:Exercises | + | [[Category:Exercises with solution]] |
Latest revision as of 17:31, 30 May 2012
Exercise 0.1.
- For which does the diagonal embedding have trivial normal bundle?
- For all , find an immersion representing the diagonal homology class with trivial normal bundle.
Hint 0.2. You may wish to look at Immersing n-spheres in 2n-space (Ex) for part 2.