2017/05/29 by Atabey Kaygun, Kaygun, Atabey, Serkan Sütlü +1
Mathematics · #19D55 #47A53 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1705.10137
openalex publication_date 2017/05/29 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We show that the (even and odd) index cocycles for theta-summable Fredholm\nmodules are in the image of the Connes-Moscovici characteristic map. To show\nthis, we first define a new range of asymptotic cohomologies, and then we\nextend the Connes-Moscovici characteristic map to our setting. The ordinary\nperiodic cyclic cohomology and the entire cyclic cohomology appear as two\ninstances of this setup. We then construct an asymptotic characteristic class,\ndefined independently from the underlying Fredholm module. Paired with the\nK-theory, the image of this class under the characteristic map yields a\nnon-zero scalar multiple of the index in the even case, and the spectral flow\nin the odd case.\n