Nigel David Higson, Dissertation Advisor/Co-Advisor Nigel David Higson, Committee Chair/Co-Chair John Roe, Committee Member Nathanial Patrick Brown, Committee Member John Collins, Committee Member
Keywords:
multiplicative index spectral triple local index
Abstract:
We consider the multiplicative property of index cocycles associated to a spectral triple. We
construct a perturbation of the JLO-cocyle and prove that it is multiplicative on the cochain
level with respect to the exterior product of theta-summable spectral triples and the product in entire cyclic theory. Furthermore, we show that this cocycle admits an asymptotic expansion if the spectral triple admits the analogue of an Euler vector field. Using Laurent series, we obtain a multiplicative local index cocycle.
