| 000 | 02298cam a2200277 i 4500 | ||
|---|---|---|---|
| 001 | 138309 | ||
| 003 | ISI Library, Kolkata | ||
| 005 | 20180510124136.0 | ||
| 008 | 160805s2017 riua b 001 0 eng | ||
| 020 | _a9781470434816 (alk. paper : pt. 1) | ||
| 040 | _aISI Library | ||
| 082 | 0 |
_a510MS _223 _bAm512 |
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| 100 | 1 |
_aFresse, Benoit, _eauthor |
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| 245 | 1 | 0 |
_aHomotopy of operads and Grothendieck-Teichmuller groups : _bpart 1: the algebraic theory and its topological background / _cBenoit Fresse. |
| 260 |
_aProvidence : _bAmerican Mathematical Society, _c©2017. |
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| 300 |
_avolums : _billustrations ; _c26 cm. |
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| 490 | 0 |
_aMathematical surveys and monographs ; _vv 217. |
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| 504 | _aIncludes bibliographical references and index. | ||
| 505 | 0 | _aPart 1. The algebraic theory and its topological background -- | |
| 520 | _aThe Grothendieck-Teichmuller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck-Teichmuller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of a rationalization process, the Malcev completion, for groups and groupoids. Most definitions are carefully reviewed in the book; it requires minimal prerequisites to be accessible to a broad readership of graduate students and researchers interested in the applications of operads. | ||
| 650 | 0 | _aHomotopy theory. | |
| 650 | 0 | _aOperads. | |
| 650 | 0 | _aGrothendieck groups. | |
| 650 | 0 | _aTeichmuller spaces. | |
| 942 |
_2ddc _cBK |
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| 999 |
_c424599 _d424599 |
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