## Syllabus on Geometry and Topology Differential Geometry

Syllabus on Geometry and Topology Differential Geometry: Basics of smooth manifolds: Inverse function theorem, implicit function theorem, submanifolds, Sard’s Theorem, embedding theorem, transversality, degree theory, integration on manifolds. Basics of matrix Lie groups over R and C: The definitions of Gl(n), SU(n), SO(n), U(n), their manifold structures, Lie