An Introduction to Geometric Topology [pdf] (unipi.it) 100 points by espeed on Dec 28, 2016 | hide | past | web | favorite | 4 comments

 From the preface:""" this book is an introduction to surfaces and three-manifolds, and to their geometrisation, due to PoincarÃ© and Koebe in 1907 in dimension two and to Thurston and Perelmann in 2002 in dimension three. Therefore this is also a textbook on low-dimensional topology, except that we completely neglect four-manifolds, that form a relevant part of this area but which do not (yet?) fit in any geometrisation perspective."""Warning: if you just want to have a look-see, skip over chapter 1. There's plenty of pictures starting in chapter 2 that give an idea of what this is all about.
 there's a nice trick in Thurston's book on 3-manifolds where you glue a strip of paper at the ends into a MÃ¶bius band and cut along the middle to get a trefoil knot out of paper.i did it with 3 and 5 twists and cut along the middle you get various knots this way`````` ----------------------------------- B___________________________________A A B ----------------------------------- `````` http://library.msri.org/books/gt3m/
 This construction makes for a nice undergrad talk. Back when I was in college, my math club held a "Brisk walk through Topology" lecture and was able to pull a fairly large audience from both the Math and CS colleges.
 Nice book, my favourite math subject, I recommend start with a more classic book, that explains the fundamentals of topology, starting from its definition. There are a lot of people talking about "topologic spaces", but, they don't know the definition, so they don't know what are they talking about.Unfortunately happens with a lot of other math concepts, for example a lot of people say "idempotent" but they don't know what does it mean and use the term for things that are not idempotents, hence the word loose its meaning.

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