Algebraic Topology
The University of New South Wales, , Prof. N J Wildberger
Updated On 02 Feb, 19
The University of New South Wales, , Prof. N J Wildberger
Updated On 02 Feb, 19
Contents:
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
4.1 ( 11 )
This lecture continues our discussion of the sphere, relating inversive geometry on the plane to the more fundamental inversive geometry of the sphere, introducing the Riemann sphere model of the complex plane with a point at infinity.
Then we discuss the sphere as the projective line over the (rational!) complex numbers.
This is the fourth lecture of this beginners course in Algebraic Topology given by N J Wildberger of UNSW. His other mathematics videos may be found at the YouTube channel njwildberger.
Sam
Sep 12, 2018
Excellent course helped me understand topic that i couldn't while attendinfg my college.
Dembe
March 29, 2019
Great course. Thank you very much.