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terrytao.wordpress.com | ||
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ncatlab.org
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| | | | | [AI summary] The Dold-Kan correspondence is a fundamental result in algebraic topology and homological algebra that establishes an equivalence between the category of simplicial abelian groups and the category of non-negatively graded chain complexes of abelian groups. This correspondence allows for the translation of problems between these two frameworks, facilitating the study of homotopy theory and homological algebra. Key aspects include its role in constructing Eilenberg-MacLane spaces, looping and delooping operations, and its applications in sheaf cohomology and computational methods. The correspondence is rooted in the work of Dold and Kan and has been generalized to various contexts, including semi-Abelian categories and stable homotopy theory. | |
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ilaba.wordpress.com
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| | | | | The Coven-Meyerowitz conjecture is a tentative characterization of finite sets that tile the integers by translations. It's also something I have been thinking about, on and off, for more than 2 decades; in the last few years, Itay Londner and I were finally able to make some progress on it. This post will provide a... | |
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gilkalai.wordpress.com
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| | | | | Topology Quasi-polynomial algorithms for telling if a knot is trivial Marc Lackenby announced a quasi-polynomial time algorithm to decide whether a given knot is the unknot! This is a big breakthrough. This question is known to be both in NP and in coNP. See this post, and updates there in the comment section. Topology seminar,... | |
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caitlinsanswersforhumanitiesclass.wordpress.com
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| | | This is the excerpt for your very first post. | ||
