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A geometric description of differential cohomology

Ulrich BunkeMatthias KreckThomas Schick — 2010

Annales mathématiques Blaise Pascal

In this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [, , , ]) 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 []. There the starting point was Quillen’s cobordism description of singular cobordism...

Comparison of Dirac operators on manifolds with

Bunke, Ulrich — 1993

Proceedings of the Winter School "Geometry and Physics"

The author introduces boundary conditions for Dirac operators D giving selfadjoint extensions such that the Hamiltonians H = D 2 define elliptic operators. Using finite propagation speed methods and assuming bounded geometry he estimates the trace of the difference of two heat operators e - t H associated to a pair of Dirac operators coinciding on cocompact sets.

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