1UFR MIG Université Paul Sabatier 118 route de Narbonne 31062 Toulouse, France 2Institutul de Matematică al Academiei Române P.O. Box 1-764 RO-014700 Bucureşti, Romania
Studia Mathematica, Tome 177 (2006) no. 2, pp. 97-112
We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from $L^p({\mit\Sigma} ^+)$ to $L^q({\mit\Sigma} ^-)$ 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 $L^2$ index. For $1+{n}/{p}-{n}/{q}\leq 0$ the index formula contains an extra term related to the Calderón projector.
Keywords:
compute index dirac operator spin riemannian manifold conical singularities acting mit sigma mit sigma obtain usual atiyah patodi singer formula spectral cut instead definition eta invariant particular reprove chous formula index leq index formula contains extra term related calder projector
Affiliations des auteurs :
André Legrand
1
;
Sergiu Moroianu
2
1
UFR MIG Université Paul Sabatier 118 route de Narbonne 31062 Toulouse, France
2
Institutul de Matematică al Academiei Române P.O. Box 1-764 RO-014700 Bucureşti, Romania
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author = {Andr\'e Legrand and Sergiu Moroianu},
title = {On the $L^p$ index of spin {Dirac} operators
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André Legrand; Sergiu Moroianu. On the $L^p$ index of spin Dirac operators
on conical manifolds. Studia Mathematica, Tome 177 (2006) no. 2, pp. 97-112. doi: 10.4064/sm177-2-1
