NOC:Introduction to Algebraic Topology - Part I

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Anant R. Shastri

NPTEL Co-ordinating Institute : IIT Bombay

NPTEL Lecture Count : 62

NPTEL Course Size : 7.0 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

Lecture 1 - Basic Problem in Topology
Lecture 2 - Concept of homotopy
Lecture 3 - Bird's eye-view of the course
Lecture 4 - Path Homotopy
Lecture 5 - Composition of paths
Lecture 6 - Fundamental group π1
Lecture 7 - Computation of Fund. Group of a circle
Lecture 8 - Computation (Continued...)
Lecture 9 - Computation concluded
Lecture 10 - Van-Kampen's Theorem
Lecture 11 - Function Spaces
Lecture 12 - Quotient Maps
Lecture 13 - Group Actions
Lecture 14 - Examples of Group Actions
Lecture 15 - Assorted Results on Quotient Spaces
Lecture 16 - Quotient Constructions Typical to Alg. Top
Lecture 17 - Quotient Constructions (Continued...)
Lecture 18 - Relative Homotopy
Lecture 19 - Construction of a typical SDR
Lecture 20 - Generalized construction of SDRs
Lecture 21 - A theoretical application
Lecture 22 - The Harvest
Lecture 23 - NDR pairs
Lecture 24 - General Remarks
Lecture 25 - Basics A ne Geometry
Lecture 26 - Abstract Simplicial Complex
Lecture 27 - Geometric Realization
Lecture 28 - Topology on |K|
Lecture 29 - Simplical maps
Lecture 30 - Polyhedrons
Lecture 31 - Point Set topological Aspects
Lecture 32 - Barycentric Subdivision
Lecture 33 - Finer Subdivisions
Lecture 34 - Simplical Approximation
Lecture 35 - Sperner Lemma
Lecture 36 - Invariance of domain
Lecture 37 - Proof of controled homotopy
Lecture 38 - Links and Stars
Lecture 39 - Homotopical Aspects of Simplicial Complexes
Lecture 40 - Homotopical Aspects
Lecture 41 - Covering Spaces and Fund. Groups
Lecture 42 - Lifting Properties
Lecture 43 - Homotopy Lifting
Lecture 44 - Relation with the fund. Group
Lecture 45 - Regular covering
Lecture 46 - Lifting Problem
Lecture 47 - Classification of Coverings
Lecture 48 - Classification
Lecture 49 - Existence of Simply connected coverings
Lecture 50 - Construction of Simply connected covering
Lecture 51 - Properties Shared by total space and base
Lecture 52 - Examples
Lecture 53 - G-coverings
Lecture 54 - Pull-backs
Lecture 55 - Classification of G-coverings
Lecture 56 - Proof of classification
Lecture 57 - Pushouts and Free products
Lecture 58 - Existence of Free Products, pushouts
Lecture 59 - Free Products and free groups
Lecture 60 - Seifert-Van Kampen Theorems
Lecture 61 - Applications
Lecture 62 - Applications (Continued...)