论文标题
Heisenberg微积分，索引理论和循环（CO）同源性
The Heisenberg Calculus, Index Theory and Cyclic (Co)homology
论文作者
论文摘要
紧凑型接触歧管上的海森伯格微积分中的低纤维化操作员是弗雷德尔姆操作员。它的符号确定了海森伯格符号的非共同代数的K理论中的一个元素。我们构建了一个周期性的环状合过程，当它与主Heisenberg符号的Connes-Chern特征配对时，它会计算索引。我们的索引公式是局部的，即根据操作员的主要符号和TM及其曲率的连接作为局部表达式。我们通过简化为Toeplitz运营商的Boutet de Monvel定理来证明我们的索引公式。
A hypoelliptic operator in the Heisenberg calculus on a compact contact manifold is a Fredholm operator. Its symbol determines an element in the K-theory of the noncommutative algebra of Heisenberg symbols. We construct a periodic cyclic cocycle which, when paired with the Connes-Chern character of the principal Heisenberg symbol, calculates the index. Our index formula is local, i.e. given as a local expression in terms of the principal symbol of the operator and a connection on TM and its curvature. We prove our index formula by reduction to Boutet de Monvel's index theorem for Toeplitz operators.
