TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols
N2  - 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.
T3  - Preprint - (2002) 20 
KW  - elliptic family
KW  - conormal symbol
KW  - spectral flow
KW  - relative index
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26386
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges
N2  - The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators.
T3  - Preprint - (2002) 24 
KW  - manifolds with edges
KW  - edge-degenerate operators
KW  - elliptic families
KW  - edge symbol
KW  - Atiyah-Bott obstruction
KW  - parameter-dependent ellipticity
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26415
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Surgery and the relative index theorem for families of elliptic operators
N2  - We prove a theorem describing the behaviour of the relative index of families of Fredholm operators under surgery performed on spaces where the operators act. In connection with additional conditions (like symmetry conditions) this theorem results in index formulas for given operator families. By way of an example, we give an application to index theory of families of boundary value problems.
T3  - Preprint - (2002) 11 
KW  - elliptic operators
KW  - index theory
KW  - surgery
KW  - relative index
KW  - boundary value problems
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26300
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators
N2  - We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.
T3  - Preprint - (2002) 14 
KW  - elliptic family
KW  - conormal symbol
KW  - relative index
KW  - index formulas
KW  - symmetry conditions
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26327
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges
N2  - Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions.
T3  - Preprint - (2002) 15 
KW  - exterior tensor product
KW  - edge-degenerate operators
KW  - elliptic families
KW  - conormal symbol
KW  - Atiyah-Bott obstruction
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26335
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Sternin, Boris
T1  - Relative elliptic theory
N2  - 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.
T3  - Preprint - (2002) 23 
KW  - Sobolev problem
KW  - elliptic morphism
KW  - (co)boundary operator
KW  - Green operator
KW  - index
KW  - Riemann-Roch theorem
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26400
ER  -