000			02287cam a2200277 i 4500
001			138310
003			ISI Library, Kolkata
005			20180510124921.0
008			160805s2017 riua b 001 0 eng
020			_a9781470434823 (alk. paper : pt. 2)
040			_aISI Library
082	0	4	_a510MS _223 _bAm512
100	1		_aFresse, Benoit, _eauthor
245	1	0	_aHomotopy of operads and Grothendieck-Teichmüller groups : _bpart 2: the applications of (rational)homotopy theory methods / _cBenoit Fresse.
260			_aProvidence : _bAmerican Mathematical Society, _c©2017.
300			_avolumes : _billustrations ; _c26 cm.
490	0		_aMathematical surveys and monographs ; _vv 217.
504			_aIncludes bibliographical references and index.
505	0		_a Part 2. The applications of (rational) homotopy theory methods --
520			_aThe 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.
650		0	_aHomotopy theory.
650		0	_aOperads.
650		0	_aGrothendieck groups.
650		0	_aTeichmuller spaces.
942			_2ddc _cBK
999			_c424600 _d424600