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 - Schulze, Bert-Wolfgang
A1 - Sternin, Boris
T1 - Localization problem in index theory of elliptic operators
N2 - This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.
T3 - Preprint - (2001) 34
KW - elliptic operators
KW - index theory
KW - surgery
KW - relative index
KW - manifold with singularities
Y1 - 2001
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26175
ER -
TY - INPR
A1 - Nazaikinskii, Vladimir
A1 - Sternin, Boris
T1 - On surgery in elliptic theory
N2 - We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.
T3 - Preprint - (2000) 22
KW - elliptic operators
KW - index theory
KW - surgery
KW - relative index
KW - manifold with singularities
Y1 - 2000
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25873
ER -
TY - INPR
A1 - Schulze, Bert-Wolfgang
A1 - Sternin, Boris
A1 - Savin, Anton
T1 - The homotopy classification and the index of boundary value problems for general elliptic operators
N2 - We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.
T3 - Preprint - (1999) 20
KW - elliptic boundary value problems
KW - Atiyah-Bott condition
KW - index theory
KW - K-theory
KW - homotopy classification
Y1 - 1999
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25568
ER -
TY - INPR
A1 - Nazaikinskii, Vladimir E.
A1 - Sternin, Boris
T1 - Surgery and the relative index in elliptic theory
N2 - We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol.
T3 - Preprint - (1999) 17
KW - elliptic operators
KW - index theory
KW - surgery
KW - relative index
KW - manifold with singularities
KW - boundary value problems
Y1 - 1999
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25538
ER -