Graphs Surfaces and Homology

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.Additional ISBNs0521766656, 0511796064, 0521154057, 9780521766654, 9780511796067, 9780521154055Graphs, Surfaces and Homology 3rd Edition is written by Peter Giblin and published by Cambridge University Press. ISBNs for Graphs, Surfaces and Homology are 9780511796067, 0511796064 and the print ISBNs are 9780521766654, 0521766656. Additional ISBNs include 0521766656, 0511796064, 0521154057, 9780521766654, 9780511796067, 9780521154055.