Surgery and Harmonic Spinors

Let M be a compact manifold with a fixed spin structure \chi. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending only on M and \chi. We show that for generic metrics on M this bound is attained.

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Field Value
Source https://hal.science/hal-00079157
Author Ammann, Bernd, Dahl, Mattias, Humbert, Emmanuel
Maintainer CCSD
Last Updated May 14, 2026, 07:31 (UTC)
Created May 14, 2026, 07:31 (UTC)
Identifier hal-00079157
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Institut Élie Cartan de Nancy (IECN) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)
creator Ammann, Bernd
date 2006-06-09T00:00:00
harvest_object_id 4c1508c5-2368-42d8-9e2c-b057763b61bc
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2025-11-04T00:00:00
set_spec type:UNDEFINED