LEADER 04301nam 22007455 450 001 9910438139303321 005 20200702165936.0 010 $a3-642-34364-3 024 7 $a10.1007/978-3-642-34364-3 035 $a(CKB)2670000000328011 035 $a(EBL)1082801 035 $a(OCoLC)827212402 035 $a(SSID)ssj0000879004 035 $a(PQKBManifestationID)11543436 035 $a(PQKBTitleCode)TC0000879004 035 $a(PQKBWorkID)10837823 035 $a(PQKB)10547829 035 $a(DE-He213)978-3-642-34364-3 035 $a(MiAaPQ)EBC6311859 035 $a(MiAaPQ)EBC1082801 035 $a(Au-PeEL)EBL1082801 035 $a(CaPaEBR)ebr10962449 035 $a(PPN)168326744 035 $a(EXLCZ)992670000000328011 100 $a20130217d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA Guide to the Classification Theorem for Compact Surfaces /$fby Jean Gallier, Dianna Xu 205 $a1st ed. 2013. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013. 215 $a1 online resource (182 p.) 225 1 $aGeometry and Computing,$x1866-6795 300 $aDescription based upon print version of record. 311 $a3-642-43710-9 311 $a3-642-34363-5 327 $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 . 330 $aThis welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology. 410 0$aGeometry and Computing,$x1866-6795 606 $aTopology 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aAlgebraic topology 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 615 0$aTopology. 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aAlgebraic topology. 615 14$aTopology. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aAlgebraic Topology. 676 $a512.55 700 $aGallier$b Jean$4aut$4http://id.loc.gov/vocabulary/relators/aut$0510781 702 $aXu$b Dianna$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438139303321 996 $aA Guide to the Classification Theorem for Compact Surfaces$92517710 997 $aUNINA