A geometric description of differential cohomology

Bunke, Ulrich, Kreck, Matthias, and Schick, Thomas. "A geometric description of differential cohomology." Annales mathématiques Blaise Pascal 17.1 (2010): 1-16. <http://eudml.org/doc/116350>.

@article{Bunke2010,
abstract = {In this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [5, 6, 7, 8]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of differential cobordism as constructed in [4]. There the starting point was Quillen’s cobordism description of singular cobordism groups for a differential manifold $X$. Here we use instead the similar description of integral cohomology from [11]. This cohomology theory is denoted by $SH^*(X)$. In this description smooth manifolds in Quillen’s description are replaced by so-called stratifolds, which are certain stratified spaces. The cohomology theory $SH^*(X)$ is naturally isomorphic to ordinary integral cohomology $H^*(X)$, thus we obtain a cobordism type definition of the differential extension of ordinary integral cohomology.},
affiliation = {NWF I - Mathematik Universität Regensburg 93040 Regensburg Deutschland; Hausdorff Research Institute for Mathematics Poppelsdorfer Allee 45 D-53115 Bonn Germany; Mathematisches Institut Georg-August-Universität Göttingen Bunsenstr. 3 37073 Göttingen Germany},
author = {Bunke, Ulrich, Kreck, Matthias, Schick, Thomas},
journal = {Annales mathématiques Blaise Pascal},
keywords = {differential cohomology; smooth cohomology; geometric cycles; cobordism; stratifold; Stokes' theorem; integration along the fiber},
language = {eng},
month = {1},
number = {1},
pages = {1-16},
publisher = {Annales mathématiques Blaise Pascal},
title = {A geometric description of differential cohomology},
url = {http://eudml.org/doc/116350},
volume = {17},
year = {2010},
}

TY - JOUR
AU - Bunke, Ulrich
AU - Kreck, Matthias
AU - Schick, Thomas
TI - A geometric description of differential cohomology
JO - Annales mathématiques Blaise Pascal
DA - 2010/1//
PB - Annales mathématiques Blaise Pascal
VL - 17
IS - 1
SP - 1
EP - 16
AB - In this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [5, 6, 7, 8]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of differential cobordism as constructed in [4]. There the starting point was Quillen’s cobordism description of singular cobordism groups for a differential manifold $X$. Here we use instead the similar description of integral cohomology from [11]. This cohomology theory is denoted by $SH^*(X)$. In this description smooth manifolds in Quillen’s description are replaced by so-called stratifolds, which are certain stratified spaces. The cohomology theory $SH^*(X)$ is naturally isomorphic to ordinary integral cohomology $H^*(X)$, thus we obtain a cobordism type definition of the differential extension of ordinary integral cohomology.
LA - eng
KW - differential cohomology; smooth cohomology; geometric cycles; cobordism; stratifold; Stokes' theorem; integration along the fiber
UR - http://eudml.org/doc/116350
ER -