The University of New South Wales, , Prof. N J Wildberger
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Updated On 02 Feb, 19
Introduction to Algebraic Topology - One-dimensional objects - Homeomorphism and the group structure on a circle - Two-dimensional surfaces: the sphere - More on the sphere - Two-dimensional objects - the torus and genus - Non-orientable surfaces - the Mobius band - The Klein bottle and projective plane - Polyhedra and Euler's formula
Applications of Euler's formula and graphs - More on graphs and Euler's formula - Rational curvature, winding and turning - Duality for polygons and the Fundamental Theorem of Algebra - More applications of winding numbers - rational curvature of a polytope - Rational curvature of polytopes and the Euler number - The geometry of surfaces - The two-holed torus and 3-crosscaps surface - Knots and surfaces I
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The Klein bottle and the projective plane are the basic non-orientable surfaces. The Klein bottle, obtained by gluing together two Mobius bands, is similar in some ways to the torus, and is something of a curiosity. The projective plane, obtained by gluing a disk to a Mobius band, is one of the most fundamental of all mathematical objects. Of all the surfaces, it most closely resembles the sphere.
This is the seventh lecture in this beginners course on Algebraic Topology, given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW.
Sep 12, 2018
Excellent course helped me understand topic that i couldn't while attendinfg my college.
March 29, 2019
Great course. Thank you very much.