Twisted cohomology
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General Introduction
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Search results
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Online References
[CDATA[http://ncatlab.org/nlab/show/twisted+cohomology
http://ncatlab.org/nlab/show/history+of+cohomology+with+local+coefficients
arXiv:1002.3004 Twists of K-theory and TMF from arXiv Front: math.AT by Matthew Ando, Andrew J. Blumberg, David Gepner We explore an approach to twisted generalized cohomology from the point of view of stable homotopy theory and quasicategory theory provided by arXiv:0810.4535. We explain the relationship to the twisted K-theory provided by Fredholm bundles. We show how our approach allows us to twist elliptic cohomology by degree four classes, and more generally by maps to the four-stage Postnikov system BO<0...4>. We also discuss Poincaré duality and umkehr maps in this setting.
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 Hopkins-Singer and later by the first author and D. Gepner with the oo-categorical treatement of twisted cohomology by Ando-Blumberg-Gepner.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 K-theory, 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
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Other Information
Stasheff sent and email to ALG-TOP on Aug 15, 2009, asking for info so that he could recover the history of twisted cohomology.
http://mathoverflow.net/questions/27567/twistings-for-other-cohomology-theories
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