Fibered cusp versus -index theory
On the index of spin Dirac operators on conical manifolds
We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from to with p,q > 1. When 1 + n/p - n/q > 0 we obtain the usual Atiyah-Patodi-Singer formula, but with a spectral cut at (n+1)/2 - n/q instead of 0 in the definition of the eta invariant. In particular we reprove Chou’s formula for the L² index. For 1 + n/p - n/q ≤ 0 the index formula contains an extra term related to the Calderón projector.
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