165 research outputs found
On the homotopy classification of elliptic operators on stratified manifolds
We find the stable homotopy classification of elliptic operators on
stratified manifolds. Namely, we establish an isomorphism of the set of
elliptic operators modulo stable homotopy and the -homology group of the
singular manifold. As a corollary, we obtain an explicit formula for the
obstruction of Atiyah--Bott type to making interior elliptic operators
Fredholm.Comment: 28 pages; submitted to Izvestiya Ross. Akad. Nau
Elliptic operators in even subspaces
In the paper we consider the theory of elliptic operators acting in subspaces
defined by pseudodifferential projections. This theory on closed manifolds is
connected with the theory of boundary value problems for operators violating
Atiyah-Bott condition. We prove an index formula for elliptic operators in
subspaces defined by even projections on odd-dimensional manifolds and for
boundary value problems, generalizing the classical result of Atiyah-Bott.
Besides a topological contribution of Atiyah-Singer type, the index formulas
contain an invariant of subspaces defined by even projections. This homotopy
invariant can be expressed in terms of the eta-invariant. The results also shed
new light on P.Gilkey's work on eta-invariants of even-order operators.Comment: 39 pages, 2 figure
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