Description

Book Synopsis


Table of Contents
  • Contents for Part 1:
  • From operads to Grothendieck-Teichmuller groups. The general theory of operads: The basic concepts of the theory of operads
  • The definition of operadic composition structures revisited
  • Symmetric monoidal categories and operads
  • Braids and $E_n$-operads: The little discs model of $E_n$-operads
  • Braids and the recognition of $E_2$-operads
  • The magma and parenthesized braid operators
  • Hopf algebras and the Malcev completion: Hopf algebras
  • The Malcev completion for groups
  • The Malcev completion for groupoids and operads
  • The operadic definition of the Grothendieck-Teichmuller group: The Malcev completion of the braid operads and Drinfeld's associators
  • The Grothendieck-Teichmuller group
  • A glimpse at the Grothendieck program
  • Appendices: Trees and the construction of free operads
  • The cotriple resolution of operads
  • Glossary of notation
  • Bibliography
  • Index
  • Contents for Part 2:
  • Homotopy theory and its applications to operads. General methods of homotopy theory: Model categories and homotopy theory
  • Mapping spaces and simplicial model categories
  • Simplicial structures and mapping spaces in general model categories
  • Cofibrantly generated model categories
  • Modules, algebras, and the rational homotopy of spaces: Differential graded modules, simplicial modules, and cosimplicial modules
  • Differential graded algebras, simplicial algebras, and cosimplicial algebras
  • Models for the rational homotopy of spaces
  • The (rational) homotopy of operads: The model category of operads in simplicial sets
  • The homotopy theory of (Hopf) cooperads
  • Models for the rational homotopy of (non-unitary) operads
  • The homotopy theory of (Hopf) $\Lambda$-cooperads
  • Models for the rational homotopy of unitary operads
  • Applications of the rational homotopy to $E_n$-operads: Complete Lie algebras and rational models of classifying spaces
  • Formality and rational models of $E_n$-operads
  • The computation of homotopy automorphism spaces of operads: Introduction to the results of the computations for the $E_n$-operads
  • The applications of homotopy spectral sequences: Homotopy spsectral sequences and mapping spaces of operads
  • Applications of the cotriple cohomology of operads
  • Applications of the Koszul duality of operads
  • The case of $E_n$-operads: The applications of the Koszul duality for $E_n$-operads
  • The interpretation of the result of the spectral sequence in the case of $E_2$-operads
  • Conclusion: A survey of further research on operadic mapping spaces and their applications: Graph complexes and $E_n$-operads
  • From $E_n$-operads to embedding spaces
  • Appendices: Cofree cooperads and the bar duality of operads
  • Glossary of notation
  • Bibliography
  • Index

Homotopy of Operads and GrothendieckTeichmuller

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    A Hardback by Benoit Fresse

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      View other formats and editions of Homotopy of Operads and GrothendieckTeichmuller by Benoit Fresse

      Publisher: MP-AMM American Mathematical
      Publication Date: 6/30/2017 12:00:00 AM
      ISBN13: 9781470434809, 978-1470434809
      ISBN10: 1470434806

      Description

      Book Synopsis


      Table of Contents
      • Contents for Part 1:
      • From operads to Grothendieck-Teichmuller groups. The general theory of operads: The basic concepts of the theory of operads
      • The definition of operadic composition structures revisited
      • Symmetric monoidal categories and operads
      • Braids and $E_n$-operads: The little discs model of $E_n$-operads
      • Braids and the recognition of $E_2$-operads
      • The magma and parenthesized braid operators
      • Hopf algebras and the Malcev completion: Hopf algebras
      • The Malcev completion for groups
      • The Malcev completion for groupoids and operads
      • The operadic definition of the Grothendieck-Teichmuller group: The Malcev completion of the braid operads and Drinfeld's associators
      • The Grothendieck-Teichmuller group
      • A glimpse at the Grothendieck program
      • Appendices: Trees and the construction of free operads
      • The cotriple resolution of operads
      • Glossary of notation
      • Bibliography
      • Index
      • Contents for Part 2:
      • Homotopy theory and its applications to operads. General methods of homotopy theory: Model categories and homotopy theory
      • Mapping spaces and simplicial model categories
      • Simplicial structures and mapping spaces in general model categories
      • Cofibrantly generated model categories
      • Modules, algebras, and the rational homotopy of spaces: Differential graded modules, simplicial modules, and cosimplicial modules
      • Differential graded algebras, simplicial algebras, and cosimplicial algebras
      • Models for the rational homotopy of spaces
      • The (rational) homotopy of operads: The model category of operads in simplicial sets
      • The homotopy theory of (Hopf) cooperads
      • Models for the rational homotopy of (non-unitary) operads
      • The homotopy theory of (Hopf) $\Lambda$-cooperads
      • Models for the rational homotopy of unitary operads
      • Applications of the rational homotopy to $E_n$-operads: Complete Lie algebras and rational models of classifying spaces
      • Formality and rational models of $E_n$-operads
      • The computation of homotopy automorphism spaces of operads: Introduction to the results of the computations for the $E_n$-operads
      • The applications of homotopy spectral sequences: Homotopy spsectral sequences and mapping spaces of operads
      • Applications of the cotriple cohomology of operads
      • Applications of the Koszul duality of operads
      • The case of $E_n$-operads: The applications of the Koszul duality for $E_n$-operads
      • The interpretation of the result of the spectral sequence in the case of $E_2$-operads
      • Conclusion: A survey of further research on operadic mapping spaces and their applications: Graph complexes and $E_n$-operads
      • From $E_n$-operads to embedding spaces
      • Appendices: Cofree cooperads and the bar duality of operads
      • Glossary of notation
      • Bibliography
      • Index

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