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 - 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 - 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 - 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 -