arXiv · math/0210462
Crossed squares and 2-crossed modules are both algebraic models for 3-types. This paper explores the interrelationships between these two models.
A. Mutlu, T. Porter. 2002-10-30. Crossed squares and 2-crossed modules. https://arxiv.org/abs/math/0210462
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The celebrated theorems of Shilov, Arens--Royden, and Forster give direct descriptions of the first three integral cohomology groups of the Gelfand spectrum of a commutative complex Banach algebra. In his 1974 ICM address, Taylor asked whether the higher cohomology groups admit descriptions in terms of the underlying ring. We give a solution to this question in even degrees: The \'etale (aka Lichtenbaum) Chow group in every codimension is canonically isomorphic to the corresponding even integral cohomology group of the Gelfand spectrum.
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