Families index for manifolds with hyperbolic cusp singularities

Details Families index for manifolds with hyperbolic cusp singularities Families index for manifolds with hyperbolic cusp singularities

2008-01-14

arxiv.org/abs/0801.1969v2

Mathematics

Differential Geometry

Changed the convention used for eta forms

Scientific paper

Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant's treatment of Dirac-type operators associated to these metrics by weaking the hypotheses on the boundary families through the use of Fredholm perturbations as in the family index theorem of Melrose and Piazza and by treating the index of families of such operators. We also extend the index theorem of Moroianu and Leichtnam-Mazzeo-Piazza to families of perturbed Dirac-type operators associated to fibered cusp metrics (sometimes known as fibered boundary metrics).

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