Algebraic Structure and Integration in Generalized Differential Cohomology

by Markus Upmeier
Doctoral thesis
Date of Examination:2013-09-30
Date of issue:2014-01-22
Advisor:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Ralf Meyer
Persistent Address: http://dx.doi.org/10.53846/goediss-4321

 

 

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Abstract

English

The present thesis deals with the construction of algebraic structure, particularly products, on generalized differential cohomology from an abstract homotopy-theoretic point of view. Beginning with a multiplicative cohomology theory E, we show that the corresponding differential cohomology groups E are multiplicative in a suitable sense. Explicit integration maps and a cocycle model for the addition are also constructed.
Keywords: Cohomology Theory; Differential Cohomology; Generalized Cohomology; Higher Category Theory; Chern Character; Differential Topology
 
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