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. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

This book presents an alternative to what the topologists refer to as “Morse-Novikov theory”, a mathematical theory which belongs to the fields of geometry and topology. The theory presented has interest in topology and dynamics, has provided inspiration and has applications outside of mathematics, especially in data analysis and shape recognitions in physics and computer science.It describes a new class of invariants associated with a generic continuous real or angle valued map defined on a compact metrizable space based on homology with coefficients in a given field. The...