Symplectic surgery and the Spin\(^c\)-Dirac operator

DOI10.1006/aima.1997.1701zbMath0929.53045arXivdg-ga/9504002OpenAlexW1976254501WikidataQ61773093 ScholiaQ61773093MaRDI QIDQ1265467

Eckhard Meinrenken

Publication date: 20 October 1999

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9504002

zbMATH Keywords

Dirac operatormoment mapindex theorysymplectic surgeryRiemann-Roch number

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Index theory and related fixed-point theorems on manifolds (58J20) Geometric quantization (53D50)

Related Items

Spinc-quantization and the K-multiplicities of the discrete series, \([Q,R=0\) and Kostant partition functions], Asymptotic dimension of invariant subspace in tensor product representation of compact Lie group, Quantisation commutes with reduction at discrete series representations of semisimple groups, Additivity of spin$^c$-quantization under cutting, Geometric quantization for proper actions, Quantization commutes with reduction, a survey, Coherent states in geometric quantization, Floer cohomology and flips, On non-Abelian symplectic cutting, Geometric quantization on CR manifolds, GEOMETRIC QUANTIZATION OF HAMILTONIAN ACTIONS OF LIE ALGEBROIDS AND LIE GROUPOIDS, RR-BS correspondence—a localization phenomenon of the index in geometric quantization, Quantization of Hamiltonian loop group spaces, Riemannian foliations and geometric quantization, Operad structures in geometric quantization of the moduli space of spatial polygons, A geometric realisation of tempered representations restricted to maximal compact subgroups, Syzygies in Equivariant Cohomology for Non-abelian Lie Groups, The multiplicities of the equivariant index of twisted Dirac operators, Hearing the weights of weighted projective planes, Atiyah-Floer conjecture: A formulation, a strategy of proof and generalizations, Torus fibrations and localization of index. III: Equivariant version and its applications, Spherical varieties and existence of invariant Kähler structures, INTERSECTION THEORY ON SYMPLECTIC QUOTIENTS OF PRODUCTS OF SPHERES, Positive scalar curvature and an equivariant Callias-type index theorem for proper actions, A \(K\)-homological approach to the quantization commutes with reduction problem, Symplectic volumes of certain symplectic quotients associated with the special unitary group of degree three, On the Vergne conjecture, Unitarity in ``Quantization commutes with reduction, \(G\)-invariant Szegő kernel asymptotics and CR reduction, Log-concavity of complexity one Hamiltonian torus actions, Moment maps and equivariant volumes, Geometric quantization for proper moment maps: the Vergne conjecture, Toeplitz operators and Hamiltonian torus actions, On perturbed two-dimensional Dirac operators, Quasi-polynomials and the singular \([Q,R=0\) theorem], Localization of the Riemann-Roch character, Formal geometric quantization. III: Functoriality in the \(\mathrm{spin}^c\) setting, Kirillov's orbit method: the case of discrete series representations, Szegö kernels, Toeplitz operators, and equivariant fixed point formulae, Quantization commutes with singular reduction: Cotangent bundles of compact Lie groups, Geometric quantization and families of inner products, Quantization of presymplectic manifolds and circle actions, Norm-square localization and the quantization of Hamiltonian loop group spaces, Kähler quantization and reduction, Formal geometric quantization, Witten Non Abelian Localization for Equivariant K-Theory, and the [𝑄,𝑅=0 Theorem], A geometric formula for multiplicities of 𝐾-types of tempered representations, Momentum maps and reduction in algebraic geometry, Quantisation of presymplectic manifolds, $K$-theory and group representations, Semifree symplectic circle actions on 4-orbifolds, Coarse geometry and Callias quantisation, 1-skeleta, Betti numbers, and equivariant cohomology, Localizing the Donaldson–Futaki invariant, Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Gauss-Bonnet theorem for \(V\)-manifolds
• Homogeneous quantization and multiplicities of group representations
• On the variation in the cohomology of the symplectic form of the reduced phase space
• Convexity properties of the moment mapping
• Geometric quantization and multiplicities of group representations
• Elliptic operators and compact groups
• The signature theorem for V-manifolds
• The Riemann-Roch theorem for complex V-manifolds
• Non-Abelian convexity by symplectic cuts
• Birational equivalence in the symplectic category
• Symplectic cuts
• Symplectic reduction and Riemann-Roch for circle actions
• The heat kernel Lefschetz fixed point formula for the spin-c dirac operator
• A new construction of symplectic manifolds
• The classification of transversal multiplicity-free group actions
• Multiplicities formula for geometric quantization. I
• Equivariant index formulas for orbifolds
• Convexity properties of the moment mapping. III
• The index of elliptic operators. I
• The index of elliptic operators. II
• The index of elliptic operators. III
• Hamiltoniens périodiques et images convexes de l'application moment
• On Coisotropic Imbeddings of Presymplectic Manifolds
• Convexity and Commuting Hamiltonians
• Cohomology rings of symplectic quotients.
• Hamiltonian torus actions on symplectic orbifolds and toric varieties
• Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field
• On Riemann-Roch Formulas for Multiplicities
• ON LOCALIZATION AND RIEMANN-ROCH NUMBERS FOR SYMPLECTIC QUOTIENTS