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Course Co-ordinated by
IIT Bombay
NPTEL
>>
Courses
>>
Mathematics
>> Algebraic Topology (Web) >>
Lecture 1: Introduction
Question in Lecture
Module 1: General Introduction
Lecture 1: Introduction
Module 2: General Topology
Lecture 2 : Preliminaries from general topology
Lecture 3 : More Preliminaries from general topology
Lecture 4 : Further preliminaries from general topology
Lecture 5 : Topological groups
Lecture 6 : Test - 1
Module 3: Fundamental groups and its basic properties
Lecture 7 : Paths, homotopies and the fundamental group
Lecture 8 : Categories and Functors
Lecture 9 : Functorial properties of the fundamental group
Lecture 10 : Brouwers theorem and its applications
Lecture 11 : Homotopies of maps. Deformation retracts
Lecture 12 & 13 : The fundamental group of the circle.
Lecture 14 : Test - II
Module 4:Theory Covering Spaces
Lecture 15 : Covering Projections
Lecture 16 : Lifting of paths and homotopies
Lecture 17 : Action of the fundamental group on the fibers
Lecture 18 : The lifting criterion
Lecture 19 : Deck transformations
Lecture 20 : Orbit Spaces
Lecture 21 : Test - III
Module 5:Seifert Van kampen Theorem & its application
Lecture 22 : Fundamental groups of certain orthogonal groups
Lecture 23 & 24 : Coproducts and push-outs
Lecture 25 : Adjunction Spaces
Lecture 26 : Seifert Van Kampen theorem
Lecture 27 : Test - IV
Module 6 :Basic Homology Theory
Lecture 28 : Introductory remarks on homology theory
Lecture 29 & 30 : The Singular chain complex and homology groups
Lecture 31 : The homology groups and their functoriality
Lecture 32 : The abelianization of the fundamental group
Lecture 33 : Homotopy invariance of homology
Lecture 34 : Small Simplicies
Lecture 35 : The Mayer Vietoris sequence and its applications
Lecture 36 : Maps of Spheres
Lecture 37 : Test - V
Module 7:Relative homology,exicism and the Jordan Brouwer separation therom
Lecture 38 : Relative homology
Lecture 39 : Excisim Theorem
Lecture 40 : Inductive limits
Lecture 41 : The Jordan-Brouwer separation theorem
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