辛代数的横截性理论、配边和不变量
Transversality theory, cobordisms, and invariants of symplectic quotients
摘要：
本文给出了辛代数不变量的理解方法。这里考虑的辛对偶是紧的辛流形（或更一般的orbifolds），它是由紧环面产生的辛流形的辛对偶。（一个配套文件审查辛代数由一个nonabel集团，显示如何减少到极大环面。设X是一个辛流形，其Hamilton作用是紧环面T.本文的主要拓扑结果描述了一个显式的协边，存在于一个辛商X的T，和一个集合的T-不动点集的组件上的迭代投影丛。这些丛的特征类可以被明确地确定，另一个结果使用这一点给出了辛商上的上同调类的积分公式，根据X的T-不动点上的数据。
英文摘要：
This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients considered here are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic manifold by a compact torus. (A companion paper examines symplectic quotients by a nonabelian group, showing how to reduce to the maximal torus.) Let X be a symplectic manifold, with a Hamiltonian action of a compact torus T. The main topological result of this paper describes an explicit cobordism that exists between a symplectic quotient of X by T, and a collection of iterated projective bundles over components of the set of T-fixed-points. The characteristic classes of these bundles can be determined explicitly, and another result uses this to give formulae for integrals of cohomology classes over the symplectic quotient, in terms of data localized at the T-fixed points of X.
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