Homotopy of operads and Grothendieck-Teichmüller groups / Benoit Fresse.

Format:

Book

Author/Creator:

Fresse, Benoit, author.

Series:

Mathematical surveys and monographs ; no. 217.

Mathematical surveys and monographs ; volume 217

Language:

English

Subjects (All):

Homotopy theory.

Operads.

Grothendieck groups.

Teichmüller spaces.

Algebraic topology--Homotopy theory--Loop space machines, operads.

Category theory; homological algebra--Homological algebra--Homotopical algebra.

Algebraic topology--Homotopy theory--Homotopy equivalences.

Algebraic topology--Homotopy theory--Rational homotopy theory.

Manifolds and cell complexes--Homology and homotopy of topological groups and related structures--Hopf algebras.

Group theory and generalizations--Permutation groups--Infinite automorphism groups.

Group theory and generalizations--Special aspects of infinite or finite groups--Braid groups; Artin groups.

Local Subjects:

Grothendieck groups.

Homotopy theory.

Operads.

Teichmüller spaces.

Algebraic topology--Homotopy theory--Loop space machines, operads.

Category theory; homological algebra--Homological algebra--Homotopical algebra.

Algebraic topology--Homotopy theory--Homotopy equivalences.

Algebraic topology--Homotopy theory--Rational homotopy theory.

Manifolds and cell complexes--Homology and homotopy of topological groups and related structures--Hopf algebras.

Group theory and generalizations--Permutation groups--Infinite automorphism groups.

Group theory and generalizations--Special aspects of infinite or finite groups--Braid groups; Artin groups.

Physical Description:

2 volumes : illustrations ; 27 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2017]

Contents:

Part 1. The algebraic theory and its topological background

I. From operads to Grothendeck-Teichmüller groups

I(a). The general theory of operads

I(b). Braids and E2-operads

I(c). Hopf algebras and the Malcev completion

I(d). The operadic definition of the Grothendieck-Teichmüller group

Part 2. The applications of (rational) homotopy theory methods

II. Homotopy theory and its applications to operads

II(a). General methods of homotopy theory

II(b). Modules, algebras, and the rational homotopy of spaces

II(c). The (rational) homotopy of operads

II(d). Applications of the rational homotopy to En-operads

III. The computation of homotopy automorphism spaces of operads

Introduction to the results of the computations for E2-operads

III(a). The applications of homotopy spectral sequences

III(b). The case of En-operads

Conclusion : a survey of further research on operadic mapping spaces and their applications.

Notes:

Includes bibliographical references and index.

ISBN:

9781470434816

1470434814

9781470434823

1470434822

OCLC:

956263920