000 03488nam a22005177a 4500
001 sulb-eb0024352
003 BD-SySUS
005 20160413122435.0
007 cr nn 008mamaa
008 130217s2013 gw | s |||| 0|eng d
020 _a9783642343643
_9978-3-642-34364-3
024 7 _a10.1007/978-3-642-34364-3
_2doi
050 4 _aQA611-614.97
072 7 _aPBP
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514
_223
100 1 _aGallier, Jean.
_eauthor.
245 1 2 _aA Guide to the Classification Theorem for Compact Surfaces
_h[electronic resource] /
_cby Jean Gallier, Dianna Xu.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXII, 178 p. 78 illus., 20 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGeometry and Computing,
_x1866-6795 ;
_v9
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 -- Proof of Proposition 5.1 -- Topological Preliminaries -- History of the Classification Theorem -- Every Surface Can be Triangulated -- Notes .
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-centred 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 _aMathematics.
650 0 _aTopology.
650 0 _aAlgebraic topology.
650 0 _aManifolds (Mathematics).
650 0 _aComplex manifolds.
650 1 4 _aMathematics.
650 2 4 _aTopology.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
650 2 4 _aAlgebraic Topology.
700 1 _aXu, Dianna.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642343636
830 0 _aGeometry and Computing,
_x1866-6795 ;
_v9
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-34364-3
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c46444
_d46444