000 | 03488nam a22005177a 4500 | ||
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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 |