C*-algebras and Elliptic Theory II

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. The results presented in this book, which is largely inspired and stimulated by the Atiyah-Singer index theorem, should be of interest to graduates and researchers in mathematical physics, differential topology and differential analysis. TOC:Preface.- Lefschetz Distribution of Lie Foliations.- Torsion as Function on the Space of Representations.- K-theory of Twisted Group Algebras.- Twisted Burnside Theorem for Two-Step Torsion-free Nilpotent Groups.- Ihara Zeta Functions for Periodic Simple Graphs.- Adiabatic Limits and the Spectrum of the Laplacian on Foliated Manifolds.- Non-standard Podle's Spheres.- Elliptic Theory on Manifolds with Corners.- Dixmier Traceability for General Pseudo-differential Operators.- Topological Invariants of Bifurcation.- L2-Invariants and Rank Metric.- Group Bundle Duality.- A New Topology on the Space of Unbounded Selfadjoint Operators.- Boundaries, Eta Invariant and the Determinant Bundle.- Modified Hochschild and Periodic Cyclic Homology.

Lefschetz Distribution of Lie Foliations.- Torsion, as a Function on the Space of Representations.- The K-theory of Twisted Group Algebras.- Twisted Burnside Theorem for Two-step Torsion-free Nilpotent Groups.- Ihara Zeta Functions for Periodic Simple Graphs.- Adiabatic Limits and the Spectrum of the Laplacian on Foliated Manifolds.- On the Non-standard Podle? Spheres.- Boundaries, Eta Invariant and the Determinant Bundle.- Elliptic Theory on Manifolds with Corners: I. Dual Manifolds and Pseudodifferential Operators.- Elliptic Theory on Manifolds with Corners: II. Homotopy Classification and K-Homology.- Dixmier Traceability for General Pseudo-differential Operators.- Topological Invariants of Bifurcation.- Modified Hochschild and Periodic Cyclic Homology.- L 2-invariants and Rank Metric.- Group Bundle Duality, Invariants for Certain C*-algebras, and Twisted Equivariant K-theory.- A New Topology on the Space of Unbounded Selfadjoint Operators, K-theory and Spectral Flow.