Witten non abelian localization for equivariant K-theory, and the [Q,R] = 0 theorem / Paul-Emile Paradan, Michéle Vergne

Von:

Paradan, Paul-Emile, 1967- [VerfasserIn]

Mitwirkende(r):

Vergne, Michèle, 1943- [VerfasserIn]

Resource type: Ressourcentyp: BuchBuchSprache: Englisch Reihen: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 261, number 1257 (September 2019)Verlag: Providence, RI : American Mathematical Society, [2019]Beschreibung: v, 71 Seiten : IllustrationenISBN:

9781470435226

Andere physische Formen: 9781470453978 | Erscheint auch als: Witten non abelian localization for equivariant K-theory, and the [Q,R] = 0 theorem. Online-Ausgabe Providence, RI : American Mathematical Society, 2019. 1 Online-Ressource (v, 71 Seiten) | Erscheint auch als: 978-1-4704-5397-8 Online-AusgabeMSC: MSC: 58J20 | 53D50 | 53C27 | 19K56 | 57S15RVK: RVK: SI 130DOI: DOI: 10.1090/memo/1257Zusammenfassung: The purpose of the present memoir is two-fold. First, the authors obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, the authors deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, the authors use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case and obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplicities of the index of general spin^c Dirac operators.PPN: PPN: 1687152144

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