Cyclic Homology

Author: Jean-Louis Loday
Publisher: Springer Science & Business Media
ISBN: 9783662217399
Release Date: 2013-06-29
Genre: Mathematics

This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.

Cyclic Homology in Non Commutative Geometry

Author: Joachim Cuntz
Publisher: Springer Science & Business Media
ISBN: 9783662064443
Release Date: 2013-03-14
Genre: Mathematics

Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.

Stacks and Categories in Geometry Topology and Algebra

Author: Tony Pantev
Publisher: American Mathematical Soc.
ISBN: 9781470415570
Release Date: 2015-06-26
Genre: Algebra

This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France. Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains. Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.

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Author:
Publisher:
ISBN: UOM:39015072604062
Release Date: 2007
Genre: Mathematics