The fundamental group and covering spaces (including classification); compact surfaces; homology theory, computations (including homotopy invariance) and applications (including Brouwer fixed point theorem).
This course is an introduction to the fundamentals of algebraic topology.
The fundamental groups, Van Kampen theorem, covering spaces, covering transformations
Homology groups, excision, Mayer-Vietoris theorem, applications, existence of nowhere vanishing vector fields, Poincare duality.
(Purnaprajna 2003 )