LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512.6
Title	Lectures on Functor Homology ([EBook]) / edited by Vincent Franjou, Antoine Touzé.
Added Personal Name	Franjou, Vincent
Added Personal Name	Touzé, Antoine
Other name(s)	SpringerLink (Online service)
Publication	Cham : Springer International Publishing , 2015.
Physical Details	VI, 149 pages: 140 illus., 1 illus. in color. : online resource.
Series	Progress in mathematics 0743-1643 ; ; 311
ISBN	9783319213057
Summary Note	This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament’s theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko’s unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert’s fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin’s strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov’s lectures highlight topological invariants: homotopy and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touzé’s introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.:
Contents note	Introduction -- A. Djament: Homologie stable des groupes à coefficients polynomiaux -- W. van der Kallen: Lectures on Bifunctors and Finite Generation of Rational Cohomology Algebras -- R. Mikhailov: Polynomial Functors and Homotopy Theory -- A. Touzé: Prerequisites of Homological Algebra.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-21305-7
Links to Related Works	Subject References: Algebraic Topology . Category Theory, Homological Algebra . Category theory (Mathematics) . Group theory . Group Theory and Generalizations . Homological algebra . Mathematics . Authors: editor . Franjou, Vincent . Touzé, Antoine . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 512.6 .

Catalogue Display

Lectures on Functor Homology

Reviews