Fibered cusp versus $d$- index theory

Details Fibered cusp versus $d$- index theory Fibered cusp versus $d$- index theory

2006-10-24

arxiv.org/abs/math/0610723v1

Mathematics

Differential Geometry

8 pages, to appear in Rendiconti Semin. Mat. Parma

Scientific paper

We prove that the indices of fibered-cusp and $d$-Dirac operators on a spin
manifold with fibered boundary coincide if the associated family of Dirac
operators on the fibers of the boundary is invertible. This answers a question
raised by Piazza. Under this invertibility assumption, our method yields an
index formula for the Dirac operator of horn-cone and of fibered horn metrics.

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