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Гомотопические группы локально конечных симплициальных множеств (в частности, конечных симплициальных комплексов) алгоритмически вычислимы (E. H. Brown).

Какая алгоритмическая сложность? Ответ зависит от того, насколько большим окажется ответ
https://kleinex.mit.edu/research/undergraduate/urop-plus/documents/2021/Allen.pdf

На второй картинке используются оценки Хуанга-Ву (на число прямых слагаемых) и Джеймса+Коэна-Мура-Нейзендорфера (на экспоненту): как следствие, порядок i-ой гомотопической группы любой нечетномерной сферы — это O(exp(i^2)).

см также:
https://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/



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Гомотопические группы локально конечных симплициальных множеств (в частности, конечных симплициальных комплексов) алгоритмически вычислимы (E. H. Brown).

Какая алгоритмическая сложность? Ответ зависит от того, насколько большим окажется ответ
https://kleinex.mit.edu/research/undergraduate/urop-plus/documents/2021/Allen.pdf

На второй картинке используются оценки Хуанга-Ву (на число прямых слагаемых) и Джеймса+Коэна-Мура-Нейзендорфера (на экспоненту): как следствие, порядок i-ой гомотопической группы любой нечетномерной сферы — это O(exp(i^2)).

см также:
https://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/

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The channel appears to be part of the broader information war that has developed following Russia's invasion of Ukraine. The Kremlin has paid Russian TikTok influencers to push propaganda, according to a Vice News investigation, while ProPublica found that fake Russian fact check videos had been viewed over a million times on Telegram. Either way, Durov says that he withdrew his resignation but that he was ousted from his company anyway. Subsequently, control of the company was reportedly handed to oligarchs Alisher Usmanov and Igor Sechin, both allegedly close associates of Russian leader Vladimir Putin. Andrey, a Russian entrepreneur living in Brazil who, fearing retaliation, asked that NPR not use his last name, said Telegram has become one of the few places Russians can access independent news about the war. "Russians are really disconnected from the reality of what happening to their country," Andrey said. "So Telegram has become essential for understanding what's going on to the Russian-speaking world." The S&P 500 fell 1.3% to 4,204.36, and the Dow Jones Industrial Average was down 0.7% to 32,943.33. The Dow posted a fifth straight weekly loss — its longest losing streak since 2019. The Nasdaq Composite tumbled 2.2% to 12,843.81. Though all three indexes opened in the green, stocks took a turn after a new report showed U.S. consumer sentiment deteriorated more than expected in early March as consumers' inflation expectations soared to the highest since 1981.
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