On the Lp index of spin Dirac operators on conical manifolds

• Autores: André Legrand, Sergiu Moroianu
• Localización: Studia mathematica, ISSN 0039-3223, Vol. 177, Nº 2, 2006, págs. 97-112
• Idioma: inglés
• DOI: 10.4064/sm177-2-1
• Texto completo no disponible (Saber más ...)
• Resumen

  • We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from Lp(_+) to Lq(_-) 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.