真映射、配边与几何量子化
Proper maps, bordism, and geometric quantization
摘要：
设$G$是作用在稳定复流形$M$上的紧致连通李群，该流形具有等变向量丛$E$ .此外，还假设$ϕ$是从$M$到李代数$\mathfrak{g}$的等变映射.我们可以在三元组$(M, E, ϕ)$上定义一些等价关系，使得等价类的集合形成阿贝尔群。本文证明了此群同构于特征标环$R(G)$的一个完备化。在此框架下，我们给出了非紧情形下“量子化可换约”猜想的几何证明。
英文摘要：
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 $\mathfrak{g}$. 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.
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