标题： 局部标准环作用的分类 显示英文标题

标题： Classification of locally standard torus actions

摘要： 一个环面 T 在流形 M 上的作用是局部标准的，如果在每个点处，稳定子是一个子环面，并且非零的等周权是其权格的基底。 然后商空间 M/T 是一个带角的流形，由所谓的单模标记装饰，该标记记录了 M 中的等周表示，并由一个系数在环面李代数积分格上的二阶上同调类，该类编码了 M 在 M/T 上的“扭曲性”。 我们根据三元组 (Q,lambda,c) 对 T 的局部标准光滑作用进行分类，其中 Q 是一个带角的流形，lambda 是一个单模标记，c 是一个系数在积分格上的二阶上同调类。 显示英文摘要

摘要： An action of a torus T on a manifold M is locally standard if, at each point, the stabilizer is a sub-torus and the non-zero isotropy weights are a basis to its weight lattice. The quotient M/T is then a manifold-with-corners, decorated by a so-called unimodular labelling, which keeps track of the isotropy representations in M, and by a degree two cohomology class with coefficients in the integral lattice of the Lie algebra of T, which encodes the "twistedness" of M over M/T. We classify locally standard smooth actions of T, up to equivariant diffeomorphisms, in terms of triples (Q,lambda,c), where Q is a manifold-with-corners, lambda is a unimodular labelling, and c is a degree two cohomology class with coefficients in the integral lattice.