02412cam a22003494a 4500 16257369 OSt 20150408114017.0 100528s2010 enka b 001 0 eng 2010022763 9780521766654 (hardback) 0521766656 (hardback) 9780521154055 (pbk.) 0521154057 (pbk.) (OCoLC)ocn642624649 DLC DLC BWK YDXCP C#P CDX BWX DLC pcc QA612 .G5 2010 514.2 22 Giblin, P. J. 14362 Graphs, surfaces and homology / Peter Giblin. 3rd ed. Cambridge ; New York : Cambridge University Press, c2010. xx, 251 p. : ill. ; 23 cm. Includes bibliographical references and index. Introduction -- Graphs -- Closed surfaces -- Simplicial complexes -- Homology groups -- The question of invariance -- Some general theorems -- Two more general theorems -- Homology modulo 2 -- Graphs in surfaces --Appendix. Abelian groups. "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"-- Algebraic topology. 14363 Cover image http://assets.cambridge.org/97805217/66654/cover/9780521766654.jpg ddc BOOK 21701 256201 0 2013-03-10 0 0 514.2 G P G 2012-05-20 EMF 00087723 EMF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 514.2 G P G 2012-05-20 EMF 00087724 EMF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 514.2 G P G 2012-06-01 SZM 00086415 SZM 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 514.2 G P G 2012-06-01 SZM 00086416 SZM 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 514.2 G P G 2012-06-03 EZF 00086990 EZF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 514.2 G P G 2012-06-03 EZF 00086991 EZF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 514.2 G P G 2012-06-04 SHF 00088104 SHF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 514.2 G P G 2012-06-04 SHF 00088105 SHF 2013-03-10 00:00:00 BOOK ddc 0