Differential cohomology

General Introduction
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Search results
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Online References
[CDATA[arXiv:1208.3961 Differential cohomology from arXiv Front: math.AT by Ulrich Bunke These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of generalized cohomology theories including products and Umkehr maps.
Axiomatic characterization of ordinary differential cohomology. James Simons and Dennis Sullivan, in Journal of Topology.
nLab on differential cohomology
arXiv:1406.3231 Twisted differential cohomology arXiv Front: math.AT by Ulrich Bunke, Thomas Nikolaus The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to (untwisted) generalized differential cohomology developed by HopkinsSinger and later by the first author and D. Gepner with the oocategorical treatement of twisted cohomology by AndoBlumbergGepner.We introduce the notion of a differential twist for a given generalized cohomology theory and construct twisted differential cohomology groups (resp. spectra). The main technical results of the paper are existence and uniqueness statements for differential twists. These results will be applied in a variety of examples, including Ktheory, topological modular forms and other cohomology theories.
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
[arXiv:1211.6832] A Bicategory Approach to Differential Cohomology from arXiv Front: math.AT by Markus Upmeier A very natural bicategory approach to differential cohomology is presented. Based on the axioms of BunkeSchick, a symmetric monoidal groupoid is associated to any differential cohomology theory. The main result is then that such a differential refinement is unique up to equivalence of the corresponding symmetric monoidal groupoids. The uniqueness results for rationallyeven theories are interpreted in this framework. Moreover, we show how the bicategory formalism may be used to give a simple construction of a differential refinement for any generalized cohomology theory.
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Other Information
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