As stated above, this is a PG level course in Mathematics, which requires basic knowledge of Linear algebra, Point set topology, and group theory.This course is central to many areas in modern mathematics. The subject itself saw tremendous growth during 1950 and currently has attained a matured status. The syllabus I have chosen is common to MA5102 at IIT Bombay and AFS-III program of National Centre for Mathematics. It has enough material common to the syllabi followed by several Universities and IIT’s in the country and goes beyond. Nevertheless it has different flavour liked by variety of students. I have published a book in which one-third of the content is roughly the present course. This book is followed by several universities abroad also for their course. INTENDED AUDIENCE :Anybody who would like to get trained in Algebraic Topology such as Computer scientists, Electrical , Aerospace engineers and mathematicians, and physicists.PREREQUISITES : Point Set Topology is pre-requisite. Exposure to Basics of Linear algebra and Group theory is preferred.INDUSTRIES SUPPORT :All IIT’s, IISERs , TIFR and Universities in India.
Week 1:What is Algebraic Topology? -An experiment with Mobius bandWeek 2:Path homotopy, Fundamental group and computation for a circle applications. Week 3:Background from Pointset topology; Quotient spaces, compact open topologyWeek 4:Relative homotopy, Typical constructions. Week 5:Convex Geometry: Simplicial ComplexesWeek 6:Subdivision and Simplicial ApproximationWeek 7:GApplicarionsWeek 8:Covering spaces: Lifting problem. Week 9:Relation with Fundamental groupsWeek 10:Seifert-Van Kampen Theorem; Free products and Free groupsWeek 11:G-coverings and ApplicationsWeek 12:Classification of Triangulated Compact Surfaces.