Degree one normal maps to the 3-sphere (Ex)
From Manifold Atlas
(Difference between revisions)
(Created page with "<wikitex>; Let $M$ be a closed oriented 3-manifold. # Prove that $M$ that there is a degree one normal map $(f, \overline f) \colon M \to S^3$ (since $\pi_3(BSO) = 0$, the tar...") |
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Let $M$ be a closed oriented 3-manifold. | Let $M$ be a closed oriented 3-manifold. | ||
| − | # Prove | + | # Prove that there is a degree one normal map $(f, \overline f) \colon M \to S^3$ (since $\pi_3(BSO) = 0$, the target bundle is trivial). |
# Prove that $(f, \overline f) \colon M \to S^3$ is normally bordant to a homotopy equivalence. | # Prove that $(f, \overline f) \colon M \to S^3$ is normally bordant to a homotopy equivalence. | ||
</wikitex> | </wikitex> | ||
[[Category:Exercises]] | [[Category:Exercises]] | ||
[[Category:Exercises without solution]] | [[Category:Exercises without solution]] | ||
Latest revision as of 05:32, 9 January 2019
Let 
be a closed oriented 3-manifold.
- Prove that there is a degree one normal map
(since 
, the target bundle is trivial).
- Prove that is normally bordant to a homotopy equivalence.
