Surgery and the spectrum of the Dirac operator
2002 (English)In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 552, 53-76 p.Article in journal (Refereed) Published
We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension greater than or equal to5 the dimension of the space of harmonic spinors is not larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order. The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension greater than or equal to3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.
Place, publisher, year, edition, pages
2002. Vol. 552, 53-76 p.
IdentifiersURN: urn:nbn:se:kth:diva-47744DOI: 10.1515/crll.2002.093ISI: 000179616800003OAI: oai:DiVA.org:kth-47744DiVA: diva2:456093
QC 201111142011-11-122011-11-122011-11-14Bibliographically approved