一元群的同伦理论及其衍生的局部化

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-03-03 DOI:10.1007/s40062-021-00276-6

Joe Chuang, Julian Holstein, Andrey Lazarev

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引用次数: 7

摘要

我们使用杆和神经结构的衍生定位来提供一些代数拓扑结果的简单证明，包括已知的和新的。这包括最近对Adams的cobar构造在非单连通情况下的推广，以及作为离散一元群的\(\infty \) -范畴的连通拓扑空间的同伦理论的一个新的代数模型。

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Homotopy theory of monoids and derived localization

We use derived localization of the bar and nerve constructions to provide simple proofs of a number of results in algebraic topology, both known and new. This includes a recent generalization of Adams’s cobar-construction to the non-simply connected case, and a new algebraic model for the homotopy theory of connected topological spaces as an \(\infty \)-category of discrete monoids.

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.