LEADER 05221nam 22006015 450 001 9910789221703321 005 20200701135537.0 010 $a1-4612-4372-6 024 7 $a10.1007/978-1-4612-4372-4 035 $a(CKB)3400000000090814 035 $a(SSID)ssj0000805503 035 $a(PQKBManifestationID)11419055 035 $a(PQKBTitleCode)TC0000805503 035 $a(PQKBWorkID)10854465 035 $a(PQKB)10966204 035 $a(DE-He213)978-1-4612-4372-4 035 $a(MiAaPQ)EBC3075264 035 $a(PPN)238068978 035 $a(EXLCZ)993400000000090814 100 $a20121227d1993 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aClassical Topology and Combinatorial Group Theory$b[electronic resource] /$fby John Stillwell 205 $a2nd ed. 1993. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1993. 215 $a1 online resource (XII, 336 p.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v72 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-97970-0 320 $aIncludes bibliographical references and index. 327 $a0 Introduction and Foundations -- 0.1 The Fundamental Concepts and Problems of Topology -- 0.2 Simplicial Complexes -- 0.3 The Jordan Curve Theorem -- 0.4 Algorithms -- 0.5 Combinatorial Group Theory -- 1 Complex Analysis and Surface Topology -- 1.1 Riemann Surfaces -- 1.2 Nonorientable Surfaces -- 1.3 The Classification Theorem for Surfaces -- 1.4 Covering Surfaces -- 2 Graphs and Free Groups -- 2.1 Realization of Free Groups by Graphs -- 2.2 Realization of Subgroups -- 3 Foundations for the Fundamental Group -- 3.1 The Fundamental Group -- 3.2 The Fundamental Group of the Circle -- 3.3 Deformation Retracts -- 3.4 The Seifert?Van Kampen Theorem -- 3.5 Direct Products -- 4 Fundamental Groups of Complexes -- 4.1 Poincaré?s Method for Computing Presentations -- 4.2 Examples -- 4.3 Surface Complexes and Subgroup Theorems -- 5 Homology Theory and Abelianization -- 5.1 Homology Theory -- 5.2 The Structure Theorem for Finitely Generated Abelian Groups -- 5.3 Abelianization -- 6 Curves on Surfaces -- 6.1 Dehn?s Algorithm -- 6.2 Simple Curves on Surfaces -- 6.3 Simplification of Simple Curves by Homeomorphisms -- 6.4 The Mapping Class Group of the Torus -- 7 Knots and Braids -- 7.1 Dehn and Schreier?s Analysis of the Torus Knot Groups -- 7.2 Cyclic Coverings -- 7.3 Braids -- 8 Three-Dimensional Manifolds -- 8.1 Open Problems in Three-Dimensional Topology -- 8.2 Polyhedral Schemata -- 8.3 Heegaard Splittings -- 8.4 Surgery -- 8.5 Branched Coverings -- 9 Unsolvable Problems -- 9.1 Computation -- 9.2 HNN Extensions -- 9.3 Unsolvable Problems in Group Theory -- 9.4 The Homeomorphism Problem -- Bibliography and Chronology. 330 $aIn recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec­ tions to other parts of mathematics which make topology an important as well as a beautiful subject. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v72 606 $aTopology 606 $aTopological groups 606 $aLie groups 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 615 0$aTopology. 615 0$aTopological groups. 615 0$aLie groups. 615 14$aTopology. 615 24$aTopological Groups, Lie Groups. 676 $a514 676 $a514/.2 700 $aStillwell$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut$041902 906 $aBOOK 912 $a9910789221703321 996 $aClassical topology and combinatorial group theory$9348503 997 $aUNINA