Elliptic operators in subspaces and the eta invariant

1999/07/31 by A. Yu. Savin, B. -W. Schulze, B. Yu. Sternin
Mathematics · #math.DG #math.AP #math.AT #math.KT #math.OA #msc:58J28 #msc:58J20 #msc:58J22 #msc:19K56

paper · pdf

published as K-theory Journal, 2002, V.26, n. 3, 253-272 · 24 pages; final version

arxiv created 2002/07/20 · arxiv updated 2009/11/30

Abstract

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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