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Homotopy of Operads and Grothendieck-Teichmuller Groups - Part 2: The Applications of (Rational) Homotopy Theory Methods (Hardcover)
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Homotopy of Operads and Grothendieck-Teichmuller Groups - Part 2: The Applications of (Rational) Homotopy Theory Methods (Hardcover)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 17 working days
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The ultimate goal of this book is to explain that the
Grothendieck-Teichmuller group, as defined by Drinfeld in quantum
group theory, has a topological interpretation as a group of
homotopy automorphisms associated to the little 2-disc operad. To
establish this result, the applications of methods of algebraic
topology to operads must be developed. This volume is devoted
primarily to this subject, with the main objective of developing a
rational homotopy theory for operads. The book starts with a
comprehensive review of the general theory of model categories and
of general methods of homotopy theory. The definition of the
Sullivan model for the rational homotopy of spaces is revisited,
and the definition of models for the rational homotopy of operads
is then explained. The applications of spectral sequence methods to
compute homotopy automorphism spaces associated to operads are also
explained. This approach is used to get a topological
interpretation of the Grothendieck-Teichmuller group in the case of
the little 2-disc operad. This volume is intended for graduate
students and researchers interested in the applications of homotopy
theory methods in operad theory. It is accessible to readers with a
minimal background in classical algebraic topology and operad
theory.
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