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- Title
Symplectic fibrations and Riemann–Roch numbers of reduced spaces.
- Authors
HAMILTON, MARK; JEFFREY, LISA
- Abstract
In this article we give formulae for the Riemann–Roch number of a symplectic quotient arising as the reduced space of a coadjoint orbit OΛ (for Λ∈g* close to 0) as an evaluation of cohomology classes over the reduced space at 0. Such a formula exhibits the dependence of the Riemann–Roch number on Λ. We also express the formula as a sum over the components of the fixed point set of the maximal torus. Our proof applies to Hamiltonian G-manifolds even if they do not have a compatible Kähler structure, using the definition of quantization in terms of the Spin-C Dirac operator.
- Subjects
RIEMANN-Roch theorems; ORBIT method; HOMOLOGY theory; TORUS; MANIFOLDS (Mathematics)
- Publication
Quarterly Journal of Mathematics, 2005, Vol 56, Issue 4, p541
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hah055