TOPOLOGY & GEOMETRY

Manifolds: Differentiable manifolds, differentiable maps and tangent  spaces,  regular values and Sard’s theorem, vector fields, submersions  and immersions, Lie  groups,  the  Lie algebra of a  Lie  group. Fundamental Groups:Homotopy of maps, multiplication of paths, the fundamental group, induced homomorphisms, the fundamental group of the circle, covering spaces, lifting theorems, the universal covering space, Seifert-Van Kampen theorem, applications.

Books

 


TOPOLOGY & GEOMETRY

Manifolds: Differentiable manifolds, differentiable maps and tangent  spaces,  regular values and Sard’s theorem, vector fields, submersions  and immersions, Lie  groups,  the  Lie algebra of a  Lie  group. Fundamental Groups:Homotopy of maps, multiplication of paths, the fundamental group, induced homomorphisms, the fundamental group of the circle, covering spaces, lifting theorems, the universal covering space, Seifert-Van Kampen theorem, applications.

Books

 


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 22 Jun 2024