欧拉示性数算子的K-同调类是平凡的
The K-homology class of the Euler characteristic operator is trivial
摘要：
在任何流形M^n上，德·拉姆算子D=d+d^*（关于完备黎曼度量），通过度的奇偶性对形式进行分次，根据卡斯帕罗夫理论在KO_0（M）中产生一个类[D]，当M是闭的时，它映射到KO_0（点）= Z中的欧拉示性数chi（M）。这个注释的目的是给出一个（也许是不幸的）事实的快速证明，即[D]是平凡的，因为它可能受到这个约束。更准确地说，如果M是连通的，[D]位于Z = KO_0（点）在KO_0（M）中的像（由包含基点引起）。
英文摘要：
On any manifold M^n, the de Rham operator D=d+d^* (with respect to a complete Riemannian metric), with the grading of forms by parity of degree, gives rise by Kasparov theory to a class [D] in KO_0(M), which when M is closed maps to the Euler characteristic chi(M) in KO_0(point) = Z. The purpose of this note is to give a quick proof of the (perhaps unfortunate) fact that [D] is as trivial as it could be subject to this constraint. More precisely, if M is connected, [D] lies in the image of Z = KO_0(point) in KO_0(M) (induced by the inclusion of a basepoint).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
