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Graphs, Surfaces and Homology - Peter Giblin

Graphs, Surfaces and Homology

(Autor)

Buch | Softcover
272 Seiten
2010 | 3rd Revised edition
Cambridge University Press (Verlag)
978-0-521-15405-5 (ISBN)
CHF 64,55 inkl. MwSt
This is an undergraduate level introduction to homology that will appeal to students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). Numerous examples and exercises are included, making this an ideal text either for teaching or for self-study.
Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.

Peter Giblin is a Professor of Mathematics (Emeritus) at the University of Liverpool.

Preface to the third edition; Preface to the first edition; List of notation; Introduction; 1. Graphs; 2. Closed surfaces; 3. Simplicial complexes; 4. Homology groups; 5. The question of invariance; 6. Some general theorems; 7. Two more general theorems; 8. Homology modulo 2; 9. Graphs in surfaces; Appendix. Abelian groups; References; Index.

Erscheint lt. Verlag 12.8.2010
Zusatzinfo Worked examples or Exercises; 150 Line drawings, black and white
Verlagsort Cambridge
Sprache englisch
Maße 151 x 227 mm
Gewicht 390 g
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte Algebraische Topologie
ISBN-10 0-521-15405-7 / 0521154057
ISBN-13 978-0-521-15405-5 / 9780521154055
Zustand Neuware
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