Self-maps of simply connected manifolds
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== Question == | == Question == | ||
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| + | Let us call an oriented closed connected manifold _flexible_ if it admits a self-map | ||
| + | that has non-trivial degree (i.e., degree not equal to 1, 0, or -1). | ||
| + | |||
{{beginthm|Question}} | {{beginthm|Question}} | ||
| − | + | Do there exist closed simply connected manifolds (of non-zero dimension) | |
| − | + | that are not flexible? | |
{{endthm}} | {{endthm}} | ||
</wikitex> | </wikitex> | ||
| − | == | + | == Examples and partial answers == |
| − | <wikitex> | + | <wikitex>; |
| − | ... | + | * Of course, all spheres are flexible. |
| + | * ... | ||
</wikitex> | </wikitex> | ||
Revision as of 22:23, 9 March 2010
Contents |
1 Question
Let us call an oriented closed connected manifold _flexible_ if it admits a self-map that has non-trivial degree (i.e., degree not equal to 1, 0, or -1).
Question 1.1.
Do there exist closed simply connected manifolds (of non-zero dimension) that are not flexible?
2 Examples and partial answers
* Of course, all spheres are flexible. * ...
3 Possible strategies
...
4 Further discussion
...
