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001			192-150601
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008			150601e20150601sz fot ||| 0|eng d
020			_a9783037196397
024	7	0	_a10.4171/139 _2doi
040			_ach0018173
072		7	_aPBFD _2bicssc
084			_a20-xx _a05-xx _a18-xx _a68-xx _2msc
100	1		_aDehornoy, Patrick, _eauthor.
245	1	0	_aFoundations of Garside Theory _h[electronic resource] / _cPatrick Dehornoy, François Digne, Eddy Godelle, Daan Krammer, Jean Michel
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2015
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2015
300			_a1 online resource (710 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aEMS Tracts in Mathematics (ETM) _v22
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_aWinner of the 2014 EMS Monograph Award! This text is a monograph in algebra, with connections toward geometry and low-dimensional topology. It mainly involves groups, monoids, and categories, and aims at providing a unified treatment for those situations in which one can find distinguished decompositions by iteratively extracting a maximal fragment lying in a prescribed family. Initiated in 1969 by F. A. Garside in the case of Artin’s braid groups, this approach turned out to lead to interesting results in a number of cases, the central notion being what the authors call a Garside family. At the moment, the study is far from complete, and the purpose of this book is both to present the current state of the theory and to be an invitation for further research. There are two parts: the bases of a general theory, including many easy examples, are developed in Part A, whereas various more sophisticated examples are specifically addressed in Part B. In order to make the content accessible to a wide audience of nonspecialists, exposition is essentially self-contained and very few prerequisites are needed. In particular, it should be easy to use the current text as a textbook both for Garside theory and for the more specialized topics investigated in Part B: Artin–Tits groups, Deligne-Lusztig varieties, groups of algebraic laws, ordered groups, structure groups of set-theoretic solutions of the Yang–Baxter equation. The first part of the book can be used as the basis for a graduate or advanced undergraduate course.
650	0	7	_aGroups & group theory _2bicssc
650	0	7	_aGroup theory and generalizations _2msc
650	0	7	_aCombinatorics _2msc
650	0	7	_aCategory theory; homological algebra _2msc
650	0	7	_aComputer science _2msc
700	1		_aDehornoy, Patrick, _eauthor.
700	1		_aDigne, François, _eauthor.
700	1		_aGodelle, Eddy, _eauthor.
700	1		_aKrammer, Daan, _eauthor.
700	1		_aMichel, Jean, _eauthor.
856	4	0	_uhttps://doi.org/10.4171/139
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/dehornoy_mini.jpg
942			_2EBK13860 _cEBK
999			_c50484 _d50484