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Oct 20, 2017 at 19:02 comment added john mangual This looks nice. I didn't pick a complicated space either $T^1 S^2 \simeq SO(3)$ is very natural. There are many natural situations where $f: M \to \mathbb{R}$ won't be quite Morse. Or we may not get to choose $f$ at all.
Oct 20, 2017 at 15:13 history edited Pietro Majer CC BY-SA 3.0
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Oct 20, 2017 at 14:16 history edited Pietro Majer CC BY-SA 3.0
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Oct 20, 2017 at 14:02 history answered Pietro Majer CC BY-SA 3.0