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ozone

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I have taken an undergraduate course in differential geometry, and graduate courses in geometrical methods in physics and general relativity. Hopefully there is a good topic available for someone with my limited knowledge. I'm open to any suggestions, but I'd like it to be something I could actually grasp and give a presentation on! Our Prof. recommended these 15 topics for a project. Perhaps one of these is relevant to physics?

(1) Topology of the Cantor set

(2) Topology of Sn and RPn

(3) Topology of simplicial complexes

(4) Topology of algebraic varieties

(5) History of the Euler characteristic

(6) Ham Sandwich theorem

(7) Hairy Ball Theorem

(8) Borsuk-Ulam Theorem

(8) Borsuk-Ulam Theorem

(9) Bolzano-Weierstrauss Property

(10) Covering spaces

(11) Proof of Fundamental Theorem of Algebra using topology

(12) Winding number

(14) Seifert van Kampen and the Fundamental groups of surfaces

(15) Poincare Conjecture