ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 58 Goette, Sebastian, Universität Freiburg, Deutschland Equivariant η-invariants and η-forms The η-invariant of a first order linear elliptic selfadjoint differential operator D is a spectral invariant of D. It appears as a boundary correction term in the Atiyah-Patodi-Singer index theorem for manifolds with boundary. Natural generalizations are equivariant η-invariants and η-forms, which appear in generalizations of the equivariant index theorem and the index theorem for families, respectively. We show that the η-forms of families with compact structure group G, induced by a G-equivariant operator D of Dirac type on the typical fibre M, and the G-equivariant η-invariant of D on M are related by a term that is locally computable on M. This result can be applied to compute ηinvariants of Dirac operators on homogeneous spaces.