Equivariant spectral flow and equivariant η-invariants on manifolds with boundary.

In this paper, we study several closely related invariants associated to Dirac operators on odd-dimensional manifolds with boundary with an action of the compact group H of isometries. In particular, the equality between equivariant winding numbers, equivariant spectral flow and equivariant Maslov indices is established. We also study equivariant η -invariants which play a fundamental role in the equivariant analog of Getzler's spectral flow formula. As a consequence, we establish a relation between equivariant η -invariants and equivariant Maslov triple indices in the splitting of manifolds. [ABSTRACT FROM AUTHOR]