From the reviews:" This is a very interesting book containing material for a comprehensive
study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras …

This book examines the differential geometry of manifolds, loop spaces, line bundles and
groupoids, and the relations of this geometry to mathematical physics. Applications …

Chen's theory of iterated integrals provides a remarkable model for the di erential forms on
the based loop space M of a di erentiable manifold M (Chen 10]; see also Hain-Tondeur 23] …

Rational homotopy is a very powerful tool for differential topology and geometry. This text
aims to provide graduates and researchers with the tools necessary for the use of rational …

This paper arose from our use of Chen's theory of iterated integrals asa tool in the study of
the complex of SX-equivariant differential forms on the free loop space LX of a manifold X …

This expository paper describes sewing conditions in two-dimensional open/closed
topological field theory. We include a description of the G-equivariant case, where G is a …

It is well-known that the periodic cyclic homology HP•(A) of an algebra A is homotopy
invariant (see Connes [3], Goodwillie [8] and Block [1]). Let A be an algebra over a field k …

Connections and curvings on gerbes are beginning to play a vital role in differential
geometry and mathematical physics--first abelian gerbes, and more recently nonabelian …

We show that every sheaf on the site of smooth manifolds with values in a stable (∞, 1)(∞,
1)-category (like spectra or chain complexes) gives rise to a “differential cohomology …

Published in two volumes, this is the first book to provide a thorough and systematic
explanation of symplectic topology, and the analytical details and techniques used in …