Welcome to this course! This page will have all the academic material related to the course. Note that administrative details like the Zoom link etc will be handled by the host institution, IIT Gandhinagar.
Here are the course details.
Dates and times for lectures: Starts from July 12th, Three lectures per week, Monday, Wednesday and Friday, 4 PM - 5:30 PM
Venue: Online (Zoom)
About the course:
This is an informal introduction to Topology and Differential Geometry for physicists. It will start by presenting a brief survey of the key ideas in elementary topology and will then go on to survey the basics of homotopy. Thereafter, differentiable manifolds will be introduced together with a survey of calculus on manifolds. We will then move on to Riemannian geometry, curvature and differential forms. In the last part we will discuss aspects of fibre bundles. Homology and cohomology may be discussed on the way if there is interest.
Day-wise lecture plans:
(Last edit - 2/8/2021.)
Lecture 1: Motivation and definition of topological space.
Lecture 2: Metric topology, basis for topology, limit points and closure, connected spaces.
Lecture 3: Compact spaces, continuity, homeomorphisms.
Lecture 4: Loops and homotopies, fundamental group.
Lecture 5: Homotopy type, contractibility, examples.
Lecture 6: Definition of differentiable manifolds, differentiation of functions.
Lecture 7: Calculus on manifolds: vector fields.
Lecture 8: Differential forms, properties of vector fields and forms.
Lecture 9: Riemannian metric, frames.
Lecture 10: Connections, curvature, torsion, isometry.
Lecture 11: Integration on manifolds, Stoke's theorem, Laplacian.
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