Classical Topology and Combinatorial Group Theory (Graduate Texts in Mathematics) (v. 72)
| Author | : | |
| Rating | : | 4.89 (592 Votes) |
| Asin | : | 0387979700 |
| Format Type | : | paperback |
| Number of Pages | : | 336 Pages |
| Publish Date | : | 2014-02-09 |
| Language | : | English |
DESCRIPTION:
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. In recent years, many students have been introduced to topology in high school mathematics. 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. 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. Pic
Does not deformation retract onto Munkres et al. This is a wonderfully intellectual, semi-historical approach to classical topology.Chapter 0 gets some fundamentals out of the way. Chapter 1 is very intriguing and contains lots of ideas. First we are given a taste of the Riemann surfaces of complex analysis. These are complemented by the nonorientable surfaces, and it all leads to the classification of surfaces, which is achieved through the fundamental group and the realisations of surfaces as polygons with identifications, and this in turn leads picturesquely to covering surfaces. These simply and concisely presented ideas provide the seeds for much of the later chapters. The . "An introduction well worth reading" according to Dr. Lee D. Carlson. Ideas from topology are now manifested everywhere in physics, engineering, computer graphics, and many, many other applications. Consequently, a thorough understanding of topology has become necessary for those who are involved in these applications. This book gives an introduction to "classical" topology that emphasizes the geometric intuition behind the subject, and is thus very suitable for those who need such an understanding. That is not to say that aspiring mathematicians will not gain from the reading of the book. It still maintains a standard of rigor that graduate students in mathematics need to advance in more in-depth c. An accessible introduction to low-dimensional topology. A Customer This book treats (geometric) topology of dimensions two and three together with necessary machinery of group theory. The account is accessible if you have the basic knowledge of general topology and algebra. It well illustrates the inherent difficulties in low-dimensional topology. A mild surprise with this book is that Novikov's proof of the unsolvability of the word problem is fully described.