arXiv subjects

Markus Upmeier

Publications and source records attributed to Markus Upmeier.

21 records · Page 2Linked to original sources

arXiv2014

Refinements of the Chern-Dold Character: Cocycle Additions in Differential Cohomology

The Chern-Dold character of a cohomology theory E is a canonical transformation $E\rightarrow HV$ 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.

math.AT↗

arXiv2013

A Bicategory Approach to Differential Cohomology

A bicategory approach to differential cohomology is presented. Based on the axioms of Bunke-Schick, a symmetric monoidal groupoid is associated to differential refinements of cohomology theories. It is proven that such differential refinements are unique up to equivalence of the corresponding symmetric monoidal groupoids and the existing uniqueness results for rationally-even 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, based on a refinement of the Chern character to a strict transformation of bicategories.

math.AT↗

arXiv2012

Products in Generalized Differential Cohomology

In this paper it is shown that multiplicative cohomology theories that are rationally even -- a technical condition that is often satisfied -- the Hopkins-Singer construction of generalized differential cohomology has a unital, graded commutative multiplicative structure. To this end, an explicit integration and a differential cohomology theory for pairs are also developed.

math.GT↗