
An Introduction to Geometric Topology [pdf] - espeed
http://www.dm.unipi.it/~martelli/Geometric_topology.pdf
======
mathgenius
From the preface:

""" 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.

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mrcactu5
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

    
    
       -----------------------------------
      B___________________________________A
      A                                   B
       -----------------------------------
    

[http://library.msri.org/books/gt3m/](http://library.msri.org/books/gt3m/)

~~~
patrickmclaren
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.

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fibo
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.

