A Combinatorial Introduction to Topology
Title | A Combinatorial Introduction to Topology PDF eBook |
Author | Michael Henle |
Publisher | Courier Corporation |
Total Pages | 340 |
Release | 1994-01-01 |
Genre | Mathematics |
ISBN | 9780486679662 |
Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
Combinatorial Algebraic Topology
Title | Combinatorial Algebraic Topology PDF eBook |
Author | Dimitry Kozlov |
Publisher | Springer Science & Business Media |
Total Pages | 416 |
Release | 2008-01-08 |
Genre | Mathematics |
ISBN | 9783540730514 |
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
Combinatorial Topology
Title | Combinatorial Topology PDF eBook |
Author | Pavel Sergeevich Aleksandrov |
Publisher | |
Total Pages | 180 |
Release | 1960 |
Genre | Combinatorial topology |
ISBN |
Foundations of Combinatorial Topology
Title | Foundations of Combinatorial Topology PDF eBook |
Author | L. S. Pontryagin |
Publisher | Courier Corporation |
Total Pages | 112 |
Release | 2015-05-20 |
Genre | Mathematics |
ISBN | 0486406857 |
Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.
An Introduction to Algebraic Topology
Title | An Introduction to Algebraic Topology PDF eBook |
Author | Andrew H. Wallace |
Publisher | Courier Corporation |
Total Pages | 212 |
Release | 2011-11-30 |
Genre | Mathematics |
ISBN | 0486152952 |
This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.
Elements of Homology Theory
Title | Elements of Homology Theory PDF eBook |
Author | Viktor Vasilʹevich Prasolov |
Publisher | American Mathematical Soc. |
Total Pages | 432 |
Release | 2007 |
Genre | Mathematics |
ISBN | 0821838121 |
The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.
Intuitive Combinatorial Topology
Title | Intuitive Combinatorial Topology PDF eBook |
Author | V.G. Boltyanskii |
Publisher | Springer Science & Business Media |
Total Pages | 153 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 1475756046 |
Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. This book is well suited for readers who are interested in finding out what topology is all about.