Displaying similar documents to “Some aspects of the De Rham complex on non-compact manifolds”

Geometric heat kernel coefficient for APS-type boundary conditions

Gorm Salomonsen (1998)

Journées équations aux dérivées partielles

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I present an alternative way of computing the index of a Dirac operator on a manifold with boundary and a special family of pseudodifferential boundary conditions. The local version of this index theorem contains a number of divergence terms in the interior, which are higher order heat kernel invariants. I will present a way of associating boundary terms to those divergence terms, which are rather local of nature.

Comparison of Dirac operators on manifolds with

Bunke, Ulrich

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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.

Elliptic operators and higher signatures

Eric Leichtnam, Paolo Piazza (2004)

Annales de l’institut Fourier

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Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov’s higher signatures on closed manifolds, - the problem of cut-and-paste invariance of Novikov’s higher signatures on closed manifolds, - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.