""" this book is an introduction to surfaces and three-manifolds,
and to their geometrisation, due to Poincaré 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 Möbius 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
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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.
""" this book is an introduction to surfaces and three-manifolds, and to their geometrisation, due to Poincaré 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.