Self-maps of simply connected manifolds

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. 
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3 Possible strategies

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4 Further discussion

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