arXiv · 1905.12632
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
Zhizhang Xie, Guoliang Yu. 2019-05-29. Higher invariants in noncommutative geometry. https://arxiv.org/abs/1905.12632
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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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