Algebraic Topology

The University of New South Wales Course , Prof. N J Wildberger

Lecture 1: AlgTop0: Introduction to Algebraic Topology

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Lecture Details :

This is the Introductory lecture to a beginner's course in Algebraic Topology given by N J Wildberger of the School of Mathematics and Statistics at UNSW in 2010.

This first lecture introduces some of the topics of the course and three problems.

Course Description :

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

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