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

• Autorzy: André Legrand , Sergiu Moroianu
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 177
• Numer: 2
• Strony: 97-112

Daty

wydano

2006

Twórcy

autor

André Legrand

• UFR MIG, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France

autor

Sergiu Moroianu

• Institutul de Matematică, al Academiei Române, P.O. Box 1-764, RO-014700 Bucureşti, Romania

Identyfikatory

DOI

10.4064/sm177-2-1