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## Main Question or Discussion Point

I have recently been assigned a project in my undergraduate topology class. I would like to do something in physics which involves topology, but I am having trouble finding a basic topic. I understand that there are some very advanced topics in string theory and the like, but I would like to find something that is more accessible.

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

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