Relative differential cohomology. (English) Zbl 1339.55003
The author studies some possible definitions of relative differential cohomology groups, generalizing the similar definition of Deligne cohomology. He obtains some long exact sequences in each case. After studying the possible definitions of relative differential cohomology for a pair of manifolds the author shows the corresponding long exact sequences. Then he constructs the Bockstein map of each exact sequence and proves the exactness. A generalization of the previous constructions is obtained for the case of maps of manifolds which are not necessarily a closed embedding.
Reviewer: Vasile Oproiu (Iaşi)
MSC:
| 55N20 | Generalized (extraordinary) homology and cohomology theories in algebraic topology |
| 53C08 | Differential geometric aspects of gerbes and differential characters |
| 58J10 | Differential complexes |
| 58A12 | de Rham theory in global analysis |
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