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Lectures on Functor Homology

Name: Lectures on Functor Homology
Brand: Birkhauser
SKU: 9783319213040
Price: 22758 HUF
Availability: InStock

Szerző: Vincent Franjou, Antoine Touzé

Nyelv:

Kötés: Kemény kötésű

Kiadó: Birkhauser

Elérhetőség: Beszállítói készleten

Küldés 10-18 napon belül

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This book features a series of lectures, that explores three different fields in which functor homol...

Információk a könyvről

Szerző

Vincent Franjou, Antoine Touzé

Nyelv

Angol

Kötés

Könyv - Kemény kötésű

Kiadva

2015

oldal

149

EAN

9783319213040

ISBN

3319213040

Enbook ID

09366223

Kiadó

Birkhauser

Súly

3613

Méretek

155 x 235 x 242

Teljes leírás

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 The series includes an intriguing development of Scorichenko's unpublished results.§§The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert's fourteenth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. By gathering these lectures, the editors hope to give the reader a feel for functors, and a valuable new perspective to apply to their favourite problems.§§

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Lectures on Functor Homology

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