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 .

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 .