Algebraic Topology (DVD)

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Media Storage Type : DVD-ROM

NPTEL Course Name : Algebraic Topology

NPTEL Subject Matter Expert : Prof. G.K. Srinivasan

NPTEL Co-ordinating Institute : IIT Bombay

NPTEL Lecture Count : 41


Lecture Titles:

Lecture 1 - Introduction
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-I
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
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
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
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
Lecture 38 - Relative homology
Lecture 39 - Excisim Theorem
Lecture 40 - Inductive limits
Lecture 41 - The Jordan-Brouwer separation theorem

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