Singular reduction and quantization
Eckhard Meinrenken,Reyer Sjamaar +1 more
213
TL;DR: In this article, it was shown that the equivariant index of a compact prequantizable manifold M is invariant to the Riemann-Roch number of the singular quotient of the manifold, provided the quotient is nonsingular.
read more
About: This article is published in Topology. The article was published on 01 Jul 1999. and is currently open access. The article focuses on the topics: Moment map & Symplectic manifold.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Between classical and quantum
Nicolaas P. Landsman
- 10 Jun 2005
TL;DR: In this article, the authors discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), and through decoherence and consistent histories.
An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg
Youliang Tian,Weiping Zhang +1 more
TL;DR: In this article, a direct analytic approach to the Guillemin-Sternberg conjecture was presented, which showed that geometric quantization commutes with symplectic reduction, which was proved recently by Meinrenken [M1, [M2] and Vergne [V1], [V2] et al.
159
Localization of the Riemann–Roch Character
TL;DR: In this paper, the authors present a K-theoretic approach to the Guillemin-Sternberg conjecture about the commutativity of geometric quantization and symplectic reduction.
135
The quantization conjecture revisited
TL;DR: In this article, a strong version of the quantization conjecture of Guillemin and Sternberg is proved for a reductive group action on a smooth, compact, polarized variety (X, L).
123
•Posted Content
Residue formulae for vector partitions and Euler-MacLaurin sums
Andras Szenes,Michèle Vergne +1 more
TL;DR: Let V be an n-dimensional real vector space endowed with a rank-n lattice Γ and ιΦ(λ) is the number of solutions of the equation ∑N k=1 xkβk = λ in nonnegative integers xk .
83
References
•Book
Introduction to Toric Varieties.
William Fulton
- 12 Jul 1993
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
3.7K
•Book
Introduction to symplectic topology
Dusa McDuff,Dietmar Salamon +1 more
- 01 Jan 1995
TL;DR: In this article, the authors present a survey of the history of classical and modern manifold geometry, from classical to modern, including linear and almost complex structures, and the Arnold conjecture of the group of symplectomorphisms.
2K
•Book
Topological methods in algebraic geometry
Friedrich Hirzebruch
- 01 Jan 1966
TL;DR: In this paper, the Riemann-Roch theorem for algebraic manifolds and complex analytic vector bundles is presented. But the authors do not consider the complexity of complex analytic line bundles.
1.5K
An introduction to symplectic topology
Claude Viterbo
- 01 Jan 1991
TL;DR: In this article, the authors show that any symplectic vector space has even dimension and any isotropic subspace is contained in a Lagrangian subspace and Lagrangians have dimension equal to half the dimension of the total space.
Convexity properties of the moment mapping. II
TL;DR: The main result of as discussed by the authors is a description of the orbit structure of a set of co-adjoint orbits in a Caf tan subalgebra of g and a positive-definite G-invariant bilinear form on $.
888