Institut für Mathematik
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- 2002 (11) (remove)
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Keywords
- conormal symbol (3)
- relative index (3)
- Atiyah-Bott obstruction (2)
- edge-degenerate operators (2)
- elliptic families (2)
- elliptic family (2)
- (co)boundary operator (1)
- Green operator (1)
- Riemann-Roch theorem (1)
- Sobolev problem (1)
Institute
When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.
Relative elliptic theory
(2002)
Relative elliptic theory
(2002)
This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms.