References

Much of this writeup is based on the wonderful book of Jeffery R. Weeks entitled The Shape of Space. It's a very engaging and easy to follow account of the topology and geometry of surfaces and 3 dimensional spaces, with a discussion of what the current state of cosmology is able to tell us about the topology and geometry of our own universe. I really can't recommend it highly enough.

For a relatively simple and beautiful proof of the topological classification of closed surfaces, see John Conway's ZIP proof.

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I wish you the best of luck in your studies of this fascinating area of mathematics.

Victor Kostyuk