Lie Models in Topology - Couverture rigide

Buijs, Urtzi; Félix, Yves; Murillo, Aniceto; Tanré, Daniel

Couverture rigide

ISBN 10 : 303054429X ISBN 13 : 9783030544294

Editeur : Springer Nature Switzerland AG, 2020

Synopsis

Since the birth of rational homotopy theory, the possibility of extending the Quillen approach - in terms of Lie algebras - to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version.

In this book, the authors develop new tools to address these problems. Working with complete Lie algebras, they construct, in a combinatorial way, a cosimplicial Lie model for the standard simplices. This is a key object, which allows the definition of a new model and realization functors that turn out to be homotopically equivalent to the classical Quillen functors in the simply connected case. With this, the authors open new avenues for solving old problems and posing new questions.

This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

Détails de l'édition

• Éditeur: Springer Nature Switzerland AG
• Date d'édition: 2020
• Langue: anglais
• ISBN 10: 303054429X
• ISBN 13: 9783030544294
• Reliure: Relié
• Nombre de pages: 308
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne