000			03210cam a22004097i 4500
001			17576454
003			OSt
005			20150820161136.0
008			121231t20132013gw a b 001 0 eng d
010			_a 2012956530
016	7		_a016187137 _2Uk
020			_a9783642343636 (alk. paper) _cEuro 22.99
035			_a(OCoLC)ocn841366265
040			_aIND _beng _cIND _erda _dMUU _dYDXCP _dDRB _dBTCTA _dUKMGB _dI8H _dBWX _dCDX _dCUD _dMNN _dOCLCF _dTOH _dOCLCQ _dDLC
042			_alccopycat
050	0	0	_aQA326 _b.G35 2013
082	0	4	_a516.352 G136G _223
100	1		_aGallier, Jean H. _95533
222			_aMathematics Collection
245	1	2	_aGuide to the Classification Theorem for Compact Surfaces _cJean Gallier, Dianna Xu.
260			_aHeidelberg: _bSpringer-Verlag, _c2013.
300			_axii, 178 pages : _billustrations (some color) ; _c24 cm.
490	1		_aGeometry and computing, _x1866-6795 ; _v9
504			_aIncludes bibliographical references and indexes.
505	0		_aThe classification theorem: informal presentation -- Surfaces -- Simplices, complexes, and triangulations -- The fundamental group, orientability -- Homology groups -- The classification theorem for compact surfaces -- Viewing the real projective plane in R³; the cross-cap and the Steiner roman surface -- Proof of proposition 5.1 -- Topological preliminaries -- History of the classification theorem -- Every surface can be triangulated.
520			_aThis welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centered approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.--
650		0	_aTopological algebras. _95534
650		0	_aClassification Theorem _96547
650		0	_aCompact Surfces _96548
650		0	_aMathematics _96549
700	1		_aXu, Dianna. _95535
830		0	_aGeometry and computing ; _v9. _95536
906			_a7 _bcbc _ccopycat _d2 _eepcn _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c6829 _d6829