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

André Legrand; Sergiu Moroianu

Studia Mathematica (2006)

  • Volume: 177, Issue: 2, page 97-112
  • ISSN: 0039-3223

Abstract

top
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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.