Explore the foundations and historical development of topology in this comprehensive 56-minute lecture. Delve into Euler's groundbreaking work on polyhedron characteristics and Descartes' early insights into curvature analysis. Examine Poincaré's contributions to understanding topological invariance and the concept of rational turn angles. Investigate Riemann's influential work on complex functions and surfaces, leading to the classification of two-dimensional surfaces. Learn about key concepts such as the Euler characteristic, homeomorphisms, and simply connected spaces. Gain insights into the Poincaré conjecture and its recent resolution. Suitable for those interested in the historical evolution of mathematical ideas and the fundamental principles of topology.
Overview
Syllabus
Topology
Euler characteristic of a polyhedron
A polyhedron homeomorphic to a torus
H. Poincare 1895
Descartes/ letter to Leibniz 1676 studied curvature of polyhedron
Rational angle version to curvature
Total curvature equals Euler characteristic
B.Riemann 1826-1866- Complex functions
Riemann surfaces
Classification of 2 dimensional surfaces
List of all compact orientable surfaces
Taught by
Insights into Mathematics
