We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from to 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-1,
author = {Andr\'e Legrand and Sergiu Moroianu},
title = {On the $L^{p}$ index of spin Dirac operators on conical manifolds},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {97-112},
zbl = {1108.58019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-1}
}
André Legrand; Sergiu Moroianu. On the $L^{p}$ index of spin Dirac operators on conical manifolds. Studia Mathematica, Tome 173 (2006) pp. 97-112. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-1/