n值映射的不动点指数公理及其应用
Axioms for the fixed point index of n-valued maps, and some applications
摘要：
给出了$n$值映射的不动点指数的一个公理化刻画.对于多面体上的$n$值映射，证明了其不动点指数关于同伦不变性、可加性和分裂性公理是唯一的。这个唯一性是用来获得简单的证明的平均公式和产品的指数公式。在流形上的$n$ -值映射的情形下，我们证明了公理可以被弱化。
英文摘要：
We give an axiomatic characterization of the fixed point index of an $n$-valued map. For $n$-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopy invariance, additivity, and a splitting property. This uniqueness is used to obtain easy proofs of an averaging formula and product formula for the index. In the setting of $n$-valued maps on a manifold, we show that the axioms can be weakened.
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