Léandre, Rémi Connes-Hida calculus in index theory. (English) Zbl 1106.58012 Zambrini, Jean-Claude (ed.), XIVth international congress on mathematical physics (ICMP 2003), Lisbon, Portugal, 28 July – 2 August 2003. Selected papers based on the presentation at the conference. Hackensack, NJ: World Scientific (ISBN 981-256-201-X/hbk). 493-497 (2005). From the introduction: There are two ways to see the relations between the index theorem and the algebraic properties of the complex auxiliary bundle associated to a Dirac operator:– The first one uses the Bismut-Chern character over the free loop space, associated to the equivariant cohomology of the free loop space.– The second one uses the cyclic complex associated to the algebra of complex valued functions on a manifold. It enters in the heart of noncommutative differential geometry of Connes.The goal of this communication is to apply tools of Hida calculus in order to understand the role of the auxiliary bundle in index theory in these two aspects.For the entire collection see [Zbl 1089.81005]. Cited in 2 Documents MSC: 58J20 Index theory and related fixed-point theorems on manifolds 46L52 Noncommutative function spaces 46L87 Noncommutative differential geometry 58J42 Noncommutative global analysis, noncommutative residues 58J65 Diffusion processes and stochastic analysis on manifolds 60H40 White noise theory PDF BibTeX XML Cite \textit{R. Léandre}, in: XIVth international congress on mathematical physics (ICMP 2003), Lisbon, Portugal, 28 July -- 2 August 2003. Selected papers based on the presentation at the conference. Hackensack, NJ: World Scientific. 493--497 (2005; Zbl 1106.58012) Full Text: Link