紧群作用的不动集置换：2ρ定理
Replacement of fixed sets for compact group actions: The 2ρtheorem
摘要：
若M和N是等变同伦等价G-流形，则不动点集M^G和N^G也是同伦等价的。置换问题提出了一个相反的问题：如果F同伦等价于固定集M^G，那么对于一个G-流形，F = N^G是否等价于M？证明了对于拓扑流形或PL流形上的局部线性作用，如果不动集的法丛是不动集的1-骨架上的复丛的两倍，则置换总是可能的.此外，我们还研究了一些具体的例子，其中的替代问题的答案范围从总是可能的刚性。
英文摘要：
If M and N are equivariantly homotopy equivalent G-manifolds, then the fixed sets M^G and N^G are also homotopy equivalent. The replacement problem asks the converse question: If F is homotopy equivalent to the fixed set M^G, is F = N^G for a G-manifold equivariantly homotopy equivalent to M? We prove that for locally linear actions on topological or PL manifolds by compact Lie groups, the replacement is always possible if the normal bundle of the fixed set is twice of a complex bundle over a 1-skeleton of the fixed set. Moreover, we also study some specific examples, where the answer to the replacement problem ranges from always possible to the rigidity.
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