Geodesic
On the $L^p$ index of spin Dirac operators on conical manifolds
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
Studia Mathematica, Tome 177 (2006) no. 2, pp. 97-112 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm177-2-1
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

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

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