Topology and Calculus of Surfaces

Code: MA640 | L-T-P-C: 3-0-0-6

Pre-requisites: MA 541 or equivalent

Combinatorial surface, classical Euler characteristic, Barycentric subdivision; Topological surfaces, Rado's theorem on the triangulability of compact surfaces, classification theorem of compact, connected surfaces; Simplicial homology, Betti numbers, Poincare's theorem on Euler characteristic; Differential surfaces, tangent spaces, vector fields, Poincare index theorem; Topological and differential manifolds.

Texts/References:

1. L.C. Kinsey, Topology of Surfaces, Springer, 1993.
2. M.A. Armstrong, Basic Topology, Springer, 2010.
3. M. Henle, A Combinatorial Introduction To Topology, Dover, 1994.