凸多胞体与Wiener-Hopf算子的指数
Convex polytopes and the index of Wiener-Hopf operators
摘要：
研究了以多面体为底的锥$Ω$上的Wiener-Hopf算子$A_Ω$的C-$^*$ -代数.如已知的，可以定义符号映射的序列，并且它们的核通过$A_Ω$的理想给出过滤，具有liminary subjectivents。可以在子对象之间定义$K$ -组值“索引映射”。这些形成由过滤引起的Atiyah-Hirzebruch型光谱序列的$E^1$项。我们表明，这个$E^1$长期可以，作为一个复杂的，被确定与细胞复合物的$P$，被认为是CW复杂的凸面作为细胞。由此可见，$A_Ω$是$KK$可收缩的，并且$A_Ω/\mathbb K$和$S$是$KK$等效的。此外，$A_Ω$的同构类是$P$的组合类型的完全不变量。
英文摘要：
We study the C$^*$-algebra of Wiener-Hopf operators $A_Ω$ on a cone $Ω$ with polyhedral base $P$. As is known, a sequence of symbol maps may be defined, and their kernels give a filtration by ideals of $A_Ω$, with liminary subquotients. One may define $K$-group valued 'index maps' between the subquotients. These form the $E^1$ term of the Atiyah-Hirzebruch type spectral sequence induced by the filtration. We show that this $E^1$ term may, as a complex, be identified with the cellular complex of $P$, considered as CW complex by taking convex faces as cells. It follows that $A_Ω$ is $KK$-contractible, and that $A_Ω/\mathbb K$ and $S$ are $KK$-equivalent. Moreover, the isomorphism class of $A_Ω$ is a complete invariant for the combinatorial type of $P$.
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