Elliptic operators in even subspaces

Details Elliptic operators in even subspaces Elliptic operators in even subspaces

1999-07-06

arxiv.org/abs/math/9907027v1

Matem. Sbornik 190, N.8, 125-160, 1999. English transl.: Sb.:Mathematics, 190, N. 8 (1999), 1195-1228

Mathematics

Differential Geometry

39 pages, 2 figures

Scientific paper

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.

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