Index theory for basic Dirac operators on Riemannian foliations

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RECERCAT Home > Centres de Recerca de Catalunya (CERCA) > Centre de Recerca Matemàtica > Prepublicacions del Centre de Recerca Matemàtica > View document

Use this identifier to quote or link this document: http://hdl.handle.net/2072/152180

dc.contributor	Centre de Recerca Matemàtica
dc.contributor.author	Brüning, Jochen
dc.contributor.author	Kamber, Franz W.
dc.contributor.author	Richardson, Ken
dc.date.accessioned	2011-07-14T08:55:04Z
dc.date.available	2011-07-14T08:55:04Z
dc.date.created	2010-11
dc.date.issued	2010-11
dc.identifier.uri	http://hdl.handle.net/2072/152180
dc.format.extent	42
dc.format.extent	430041 bytes
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Centre de Recerca Matemàtica
dc.relation.ispartofseries	Prepublicacions del Centre de Recerca Matemàtica;981
dc.rights	Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/)
dc.subject.other	Foliacions (Matemàtica)
dc.subject.other	Índex, Teoria d' (Matemàtica)
dc.title	Index theory for basic Dirac operators on Riemannian foliations
dc.type	info:eu-repo/semantics/preprint
dc.subject.udc	514 - Geometria
dc.description.abstract	In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

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