Intuitive Combinatorial Topology (Universitext) 1st Edition by V.G. Boltyanskii (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The material covered in this book is rather outdated — the first two-thirds of the book focuses on the topology of curves and surfaces, which people studied in the 19th century. Then in the last third, it tries to cover as much early twentieth-century topology as possible, with mixed results. On the other hand, 19th century topology is fun. Modern topology tends to involve very abstract heavy machinery, at the cost of being able to play with simple, very geometric structures.A high school student or young undergraduate would greatly enjoy this book — it is filled with beautiful pictures, with very intuitive proofs of some basic but important theorems. The numerous exercises are also great for building geometric intuition for classical topology. But, largely due to the outdatedness of the material, an advanced undergraduate or beginning graduate student who is looking for a book with (admittedly far fewer) pretty pictures would be better off reading more modern texts like Guillemin and Pollack’s

⭐Hatcher’s

⭐.

⭐This short, elementary survey of topology is meant to be accessible for the most part to high school students and beginning undergraduates. I hope that such unspoiled souls will have the courage to be dissatisfied at least with the first chapter, since it cares only about concepts (continuity, homeomorphism, etc.) while offering little substance, and also there is the usual overemphasis of the Jordan curve theorem and pathological curves. Young people should not be tricked into thinking that topology has been built around such silly things. But in the other two chapters we get to actual topology, and all the usual stuff is here: Euler characteristic, classification of surfaces, knots, the fundamental group, homology, etc. Each topic is treated in a relatively sensible, swift manner; rather too swift towards the end, I think, when there seems to be a race to include as many topological concepts as possible, with little concern for what would be the most natural or interesting way to proceed (of course this does not have to be a bad thing if one is using the book as a down-to-earth complement to a formal textbook).

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