Elements of Combinatorial and Differential Topology
About this Title
V. V. Prasolov, Independent University of Moscow, Moscow, Russia. Translated by Olga Sipacheva
Publication: Graduate Studies in Mathematics
Publication Year: 2006; Volume 74
ISBNs: 978-0-8218-3809-9 (print); 978-1-4704-1153-4 (online)
MathSciNet review: MR2233951
MSC: Primary 57-01
Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed.
One of the main goals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology.
The book contains many problems; almost all of them are supplied with hints or complete solutions.
Advanced undergraduates and graduate students interested in combinatorial and differential topology.
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