Elliptic operators in subspaces and the eta invariant

Details Elliptic operators in subspaces and the eta invariant Elliptic operators in subspaces and the eta invariant

1999-07-08

arxiv.org/abs/math/9907047v2

K-theory Journal, 2002, V.26, n. 3, 253-272

Mathematics

Differential Geometry

24 pages; final version

Scientific paper

The spectral eta-invariant of a self-adjoint elliptic differential operator on a closed manifold is rigid, provided that the parity of the order is opposite to the parity of dimension of the manifold. The paper deals with the calculation of the fractional part of the eta-invariant in this case. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces. It also utilizes K-theory with coefficients Z_n. In particular, it is shown that the group K(T^*M,Z_n) is realized by elliptic operators (symbols) acting in appropriate subspaces.

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