Cyclic homology in a special world

Bjørn Ian Dundas ()
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Bjørn Ian Dundas: University of Bergen

A chapter in Advances in Noncommutative Geometry, 2019, pp 291-319 from Springer

Abstract: Abstract In work of Connes and Consani, Γ-spaces have taken a new importance. Segal introduced Γ-spaces in order to study stable homotopy theory, but the new perspective makes it apparent that also information about the unstable structure should be retained. Hence, the question naturally presents itself: to what extent are the commonly used invariants available in this context? We offer a quick survey of (topological) cyclic homology and point out that the categorical construction is applicable also in an ℕ $${\mathbb N}$$ -algebra (aka. semi-ring or rig) setup.

Keywords: Cyclic homology; Ring spectra; Topological cyclic homology; Special gamma spaces; Unstable homology; Group completion; Primary: 13D03; Secondary: 18G60, 19D55, 55P92 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-29597-4_5

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DOI: 10.1007/978-3-030-29597-4_5

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