Filtern
Volltext vorhanden
- ja (22)
Dokumenttyp
- Preprint (22)
Sprache
- Englisch (22) (entfernen)
Gehört zur Bibliographie
- nein (22) (entfernen)
Schlagworte
- K-theory (7)
- Atiyah-Patodi-Singer theory (5)
- conormal symbol (3)
- eta invariant (3)
- index (3)
- index of elliptic operators in subspaces (3)
- Atiyah-Bott obstruction (2)
- Fredholm property (2)
- boundary value problem (2)
- boundary value problems (2)
- edge-degenerate operators (2)
- elliptic families (2)
- elliptic family (2)
- elliptic operator (2)
- eta-invariant (2)
- linking coefficients (2)
- modn-index (2)
- relative index (2)
- spectral flow (2)
- symmetry conditions (2)
- Atiyah-Bott condition (1)
- Chern character (1)
- Dirac operators (1)
- Pontrjagin duality (1)
- covering (1)
- dimension functional (1)
- edge symbol (1)
- elliptic boundary value problems (1)
- elliptic operators (1)
- elliptic operators in subspaces (1)
- elliptic problem (1)
- exterior tensor product (1)
- finiteness theorem (1)
- homotopy classification (1)
- index formula (1)
- index formulas (1)
- index of elliptic operator (1)
- index theory (1)
- manifold with edge (1)
- manifolds with edges (1)
- mod k index (1)
- modulo n index (1)
- nonlocal problem (1)
- parameter-dependent ellipticity (1)
- parity condition (1)
- parity conditions (1)
- problem of classification (1)
- pseudodifferential subspace (1)
- pseudodifferential subspaces (1)
- relative η-invariant (1)
- spectral boundary value problems (1)
- η-invariant (1)
Institut
In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms.
The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.
The homotopy classification and the index of boundary value problems for general elliptic operators
(1999)
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.
An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.
An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.
The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented.
The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincaré duality in the K-theory of the corresponding manifolds with singularities.
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.