000			02342 a2200253 4500
008			240328b |||||||| |||| 00| 0 eng d
020			_a9781461287490
082			_a514 STI
100			_aStillwell, John
245			_aClassical topology and combinatorial group theory
250			_a2nd ed.
260			_aNew York: _bSpringer, _c1993.
300			_axii, 334p.: _bill.;pbk.: _c23cm.
440			_aGraduate Texts in Mathematics
504			_aIncludes Bibliography and Chronology and Index
520			_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. https://link.springer.com/book/10.1007/978-1-4612-4372-4#about-this-book
650			_aAbelian Group
650			_aGroup Theory
650			_aTopology
650			_aEuler's Polyhedron Formula
650			_aCombinatorial Group Theory
650			_aGraphs and Free Groups
942			_cTD _2ddc
999			_c60117 _d60117