Question
This technique involves replacing a copy of S-r times D-n-minus-r with D-r-plus-one times S-n-minus-r-minus-one, which has the same boundary. For 10 points each:
[10m] Name this technique of “spherical modification” introduced by John Milnor. To prove the Poincaré conjecture, Grigori Perelman employed Ricci flow with this technique.
ANSWER: surgery
[10e] This quantity for a 2-manifold is the minimal number of surgeries required to reduce it to the 2-sphere. Handlebodies are identified up to homeomorphism by this quantity that determines how many holes they have.
ANSWER: genus [prompt on g]
[10h] Handle cancellation via this technique is employed in Stephen Smale’s proof of the h-cobordism theorem. Use of this technique, which arises from a namesake “embedding theorem,” helped to lay the foundations of surgery theory.
ANSWER: Whitney trick [prompt on Whitney embedding theorem]
<Jeremy Cummings and David Bass, Other Science - Mathematics>
Summary
| 2023 Chicago Open | 08/05/2023 | Y | 9 | 16.67 | 100% | 67% | 0% |
Data
| BHSU | Saint Peter Andre 3000 | 0 | 10 | 0 | 10 |
| Curse you, Periplus the Platypus! | In Search of Things Past | 10 | 10 | 0 | 20 |
| remembrance of lost time | Don't be Afraid, the Clown's Afraid Too | 10 | 10 | 0 | 20 |
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| I prefer really not to speak. If I speak I’m in big trouble | I would prefer not to | 10 | 10 | 0 | 20 |
| Romanos IV Diogenes’ Macaroni Grill | Quasicrystal Silence | 0 | 10 | 0 | 10 |
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