PH60405: Topology And Geometry For Physicists

PH60405
Course name	Topology And Geometry For Physicists
Offered by	Physics
Credits	3
L-T-P	3-0-0
Previous Year Grade Distribution
{{{grades}}}
Semester	Spring

Syllabus

Syllabus mentioned in ERP

Topology: Preliminaries; Topological spaces; Closed sets and limit points; Hausdorff spaces; Continuous functions and Homeomorphisms; Metric topology; Connectedness and Compactness; Heine-borel Theorem; Homotopy of paths; The fundamental group; Covering spaces; Fundamental groups of circle, punctured plane, S^n and surfaces; Higher homotopy groups; Vector fields and fixed points. Differential Geometry: Definition of a manifold; Differentiation of functions, Orientability; Calculus on manifolds; Diffrential forms; Riemannian geometry; Frames; Connections; Curvature and Torsion; Volume form; Isometry; Integration of differential forms; Exterior differentiation; Stokes theorem; The Laplacian on forms; Homology and Cohomology- Simplicial homology; De Rham cohomology; Harmonic forms; Fibre bundles; Tangent and Cotangent bundles; Vector bundles and Principal bundles.