Topology For Beginners Introduction To 3D Manifolds

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I give a gentle introduction to three dimensional manifolds by discussing simple surfaces, and how they can be generalized. • Our universe is a 3D manifold, and so understanding what kinds of topologies three dimensional manifolds can exist is crucial for cosmology. It also teaches us about what other kinds of universes could be like. This leads to a discussion of the hyper torus, the 'hyper Klien bottle' and the 'twisted hyper torus'. • Resources: • https://sites.google.com/site/richard... • The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds (Jeffrey R. Weeks) • Shape of Space - Topology and Geometry Software • http://www.geometrygames.org/SoS/

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