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

André Legrand, and Sergiu Moroianu. "On the $L^{p}$ index of spin Dirac operators on conical manifolds." Studia Mathematica 177.2 (2006): 97-112. <http://eudml.org/doc/284600>.

@article{AndréLegrand2006,
abstract = {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.},
author = {André Legrand, Sergiu Moroianu},
journal = {Studia Mathematica},
keywords = {Dirac operator; spin conical manifold; index theorem; eta invariant},
language = {eng},
number = {2},
pages = {97-112},
title = {On the $L^\{p\}$ index of spin Dirac operators on conical manifolds},
url = {http://eudml.org/doc/284600},
volume = {177},
year = {2006},
}

TY - JOUR
AU - André Legrand
AU - Sergiu Moroianu
TI - On the $L^{p}$ index of spin Dirac operators on conical manifolds
JO - Studia Mathematica
PY - 2006
VL - 177
IS - 2
SP - 97
EP - 112
AB - 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.
LA - eng
KW - Dirac operator; spin conical manifold; index theorem; eta invariant
UR - http://eudml.org/doc/284600
ER -