https://arxiv.org/abs/2406.19326 пишут, что окончательно описали гомотопическую неинвариантность струнного коумножения в терминах кручения Уайтхеда! Работа на 63 страницы, (зачем-то) использует язык бесконечность-категорий. #чётамнаархиве
струнная топология изучает богатую структуру на гомологиях свободных пространств петель гладких замк.ориент. многообразий. часть этой структуры — струнное коумножение. другие операции струнной топологии — струнное умножение и дифференциал, задаваемый "вращением петель", — гомотопически инвариантны. Даже, если правильно помню, определены и для комплексов Пуанкаре)
https://arxiv.org/abs/2406.19326 пишут, что окончательно описали гомотопическую неинвариантность струнного коумножения в терминах кручения Уайтхеда! Работа на 63 страницы, (зачем-то) использует язык бесконечность-категорий. #чётамнаархиве
струнная топология изучает богатую структуру на гомологиях свободных пространств петель гладких замк.ориент. многообразий. часть этой структуры — струнное коумножение. другие операции струнной топологии — струнное умножение и дифференциал, задаваемый "вращением петель", — гомотопически инвариантны. Даже, если правильно помню, определены и для комплексов Пуанкаре)
At this point, however, Durov had already been working on Telegram with his brother, and further planned a mobile-first social network with an explicit focus on anti-censorship. Later in April, he told TechCrunch that he had left Russia and had “no plans to go back,” saying that the nation was currently “incompatible with internet business at the moment.” He added later that he was looking for a country that matched his libertarian ideals to base his next startup. But Telegram says people want to keep their chat history when they get a new phone, and they like having a data backup that will sync their chats across multiple devices. And that is why they let people choose whether they want their messages to be encrypted or not. When not turned on, though, chats are stored on Telegram's services, which are scattered throughout the world. But it has "disclosed 0 bytes of user data to third parties, including governments," Telegram states on its website. Some people used the platform to organize ahead of the storming of the U.S. Capitol in January 2021, and last month Senator Mark Warner sent a letter to Durov urging him to curb Russian information operations on Telegram. Again, in contrast to Facebook, Google and Twitter, Telegram's founder Pavel Durov runs his company in relative secrecy from Dubai. Right now the digital security needs of Russians and Ukrainians are very different, and they lead to very different caveats about how to mitigate the risks associated with using Telegram. For Ukrainians in Ukraine, whose physical safety is at risk because they are in a war zone, digital security is probably not their highest priority. They may value access to news and communication with their loved ones over making sure that all of their communications are encrypted in such a manner that they are indecipherable to Telegram, its employees, or governments with court orders.
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