THE LOOP GROUP AND THE COBAR CONSTRUCTION
THE LOOP GROUP AND THE COBAR CONSTRUCTION
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LOOP 组和 COBAR 结构
DOI：
10.1090/s0002-9939-09-10238-1
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Tonks
中科院分区：
文献类型：
--
作者：
K. Hess;A. Tonks
我们证明，对于任何1 - 约化单纯集\(X\)，亚当斯的上棒构造（作用于\(X\)的正规化链复形）自然是坎环群\(GX\)上的正规化链\(CGX\)的强形变收缩核，这为应用同调代数工具将代数结构的扰动从后者转移到前者提供了可能性。为了证明我们的定理，我们扩展了上棒构造的定义，并实际上得到了对于所有0 - 约化单纯集都存在这样一个强形变收缩核。
We prove that for any 1-reduced simplicial set X, Adams' cobar construction, on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX, opening up the possibility of applying the tools of homological algebra to transfering perturbations of algebraic structure from the latter to the former. In order to prove our theorem, we extend the definition of the cobar construction and actually obtain the existence of such a strong deformation retract for all 0-reduced simplicial sets.