Institute for Mathematical Physics the Local Index Formula in Semifinite Von Neumann Algebras I: Spectral Flow the Local Index Formula in Semifinite Von Neumann Algebras I: Spectral Flow the Local Index Formula in Semifinite Von Neumann Algebras I: Spectral Flow
Institute for Mathematical Physics the Local Index Formula in Semifinite Von Neumann Algebras I: Spectral Flow the Local Index Formula in Semifinite Von Neumann Algebras I: Spectral Flow the Local Index Formula in Semifinite Von Neumann Algebras I: Spectral Flow
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通讯作者：
A. Carey;J. Phillips;A. Rennie;F. Sukochev
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作者：
A. Carey;J. Phillips;A. Rennie;F. Sukochev
所有作者都得到了ARC(澳大利亚)和NSERC(加拿大)的资助，此外，第三位作者获得了纽卡斯尔大学早期职业研究人员的资助，第一位作者获得了开始这项研究的克莱数学研究所的支持，并得到了欧文·薛定谔研究所的非对易几何项目的支持。本文将Connes和Moscovici的局部指数公式推广到一般半定von Neumann代数的*-子代数A的谱三元组的情形。在这一背景下，它给出了连接无界自伴Breuer-Fredholm型算子(隶属于von Neumann代数)和酉等价型算子的路径上的谱流的公式。即使在原定理的背景下，我们的证明也是新颖的，并且依赖于在A的循环上同调中引入一个函数值上循环，它几乎是a(b，B)-上循环。
All authors were supported by grants from ARC (Australia) and NSERC (Canada), in addition the third named author acknowledges a University of Newcastle early career researcher grant and the first named author acknowledges the Clay Mathematics Institute for whom this research was begun and support from the Erwin Schrödinger Institute's Noncommutative Geometry program. Abstract We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an unbounded self adjoint Breuer-Fredholm operator, affiliated to the von Neumann algebra, to a unitarily equivalent operator. Our proof is novel even in the setting of the original theorem and relies on the introduction of a function valued cocycle which is 'almost' a (b, B)-cocycle in the cyclic cohomology of A.