Refinements of the Chern-Dold character: cocycle additions in differential cohomology

Markus Upmeier

doi:10.1007/s40062-015-0106-y

Refinements of the Chern-Dold character: cocycle additions in differential cohomology

Markus Upmeier

Mathematical Science

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

The Chern-Dold character of a cohomology theory E is a canonical transformation E→HV to ordinary cohomology. A spectrum representing E gives homotopy theoretic cocycles for E, while HV can be represented by singular cocycles. We construct a refinement of the Chern-Dold character to a transformation of the cocycle categories that takes the homotopical composition to the addition of singular cocycles. This is applied to construct additive structures at the level of differential cocycles for generalized differential cohomology.

Original language	English
Pages (from-to)	291-307
Journal	Journal of Homotopy and Related Structures
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s40062-015-0106-y
Publication status	Published - 24 Apr 2015

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title = "Refinements of the Chern-Dold character: cocycle additions in differential cohomology",

abstract = "The Chern-Dold character of a cohomology theory E is a canonical transformation E→HV to ordinary cohomology. A spectrum representing E gives homotopy theoretic cocycles for E, while HV can be represented by singular cocycles. We construct a refinement of the Chern-Dold character to a transformation of the cocycle categories that takes the homotopical composition to the addition of singular cocycles. This is applied to construct additive structures at the level of differential cocycles for generalized differential cohomology.",

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AB - The Chern-Dold character of a cohomology theory E is a canonical transformation E→HV to ordinary cohomology. A spectrum representing E gives homotopy theoretic cocycles for E, while HV can be represented by singular cocycles. We construct a refinement of the Chern-Dold character to a transformation of the cocycle categories that takes the homotopical composition to the addition of singular cocycles. This is applied to construct additive structures at the level of differential cocycles for generalized differential cohomology.

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DO - 10.1007/s40062-015-0106-y

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JO - Journal of Homotopy and Related Structures

JF - Journal of Homotopy and Related Structures

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ER -

Refinements of the Chern-Dold character: cocycle additions in differential cohomology

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