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

André Legrand; Sergiu Moroianu

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arXiv · math/0407027

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

André Legrand·Sergiu Moroianu

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Abstract

We compute the index of the Dirac operator on spin Riemannian manifolds with conical singularities, acting from $L^p(Σ^+)$ to $L^q(Σ^-)$ with $p,q>1$. When $1+\frac{n}{p}-\frac{n}{q}>0$ we obtain the usual Atiyah-Patodi-Singer formula, but with a spectral cut at $\frac{n+1}{2}-\frac{n}{q}$ instead of 0 in the definition of the eta invariant. In particular we reprove Chou's formula for the $L^2$ index. For $1+\frac{n}{p}-\frac{n}{q}\leq 0$ the index formula contains an extra term related to the Calderón projector.

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BibTeX RIS

André Legrand, Sergiu Moroianu. 2004-07-02. On the $L^p$ index of spin Dirac operators on conical manifolds. https://arxiv.org/abs/math/0407027

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