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On the $L^{p}$ index of spin Dirac operators on conical manifolds

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Legrand A., Moroianu S.

Studia Mathematica

2006

tom 177

nr 2

97-112

We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from $L^{p}(Σ⁺)$ to $L^{q}(Σ¯)$ 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.

Ograniczanie wyników

1 Studia Mathematica

1 Legrand A.

1 Moroianu S.

1 2006

Wyniki wyszukiwania

On the $L^{p}$ index of spin Dirac operators on conical manifolds