2012/06/23 by Yanli Song, Song, Yanli
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG) #math.DG #math.KT #math.SG
paper · pdf · doi:10.48550/arxiv.1206.5403
30 pages
openalex publication_date 2012/06/23 · arxiv created 2013/01/22 · arxiv updated 2013/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a compact connected Lie group acting on a stable complex manifold M with equivariant vector bundle E. Besides, suppose ϕ is an equivariant map from M to the Lie algebra \mathfrakg. We can define some equivalence relation on the triples (M, E, ϕ) such that the set of equivalence classes form an abelian group. In this paper, we will show that this group is isomorphic to a completion of character ring R(G). In this framework, we provide a geometric proof to the "Quantization Commutes with Reduction" conjecture in the non-compact setting.