Introduction to Algebraic Topology (Part_I) GZX06CWW0R

URI	`m2://res/GZX06CWW0R`
Kind	course
Creators	Anant R. Shastri (instructor)
Date	2021-01-08
Scope	in
Ids	course 02qyf5152:111101144

Expressions

e1: edition

Language	en
Date	2021-01-08

m1: page, IIT Bombay (record). nptel 111101144
m2: page, 2021-01-08 (record). nptel 111101144

Contents

part 1: Week 1
session 1: Lecture 1 : Basic Problem in Topology
session 2: Lecture 2 : Concept of homotopy
session 3: Lecture 3 : Bird's eye-view of the course
session 4: Lecture 4 : Path Homotopy
session 5: Lecture 5 : Composition of paths
session 6: Lecture 6 : Fundamental group Ï€1
part 2: Week 2
session 7: Lecture 7 : Computation of Fund. Group of a circle
session 8: Lecture 8 : Computation continued
session 9: Lecture 9 : Computation concluded
session 10: Lecture 10 : Van-Kampen's Theorem
session 11: Lecture 11 : Function Spaces
session 12: Lecture 12 : Quotient Maps
part 3: Week 3
session 13: Lecture 13 : Group Actions
session 14: Lecture 14 : Examples of Group Actions
session 15: Lecture 15 : Assorted Results on Quotient Spaces
session 16: Lecture 16 : Quotient Constructions Typical to Alg. Top.
session 17: Lecture 17 : Quotient Constructions continued
part 4: Week 4
session 18: Lecture 18 : Relative Homotopy
session 19: Lecture 19 : Construction of a typical SDR
session 20: Lecture 20 : Generalized construction of SDRs
session 21: Lecture 21 : A theoretical application
session 22: Lecture 22 : The Harvest
part 5: Week 5
session 23: Lecture 23 : NDR pairs
session 24: Lecture 24 : General Remarks
session 25: Lecture 25 : Basics A ne Geometry
session 26: Lecture 26 : Abstract Simplicial Complex
session 27: Lecture 27 : Geometric Realization
part 6: Week 6
session 28: Lecture 28 : Topology on |K|
session 29: Lecture 29 : Simplical maps
session 30: Lecture 30 : Polyhedrons
session 31: Lecture 31 : Point Set topological Aspects
session 32: Lecture 32 : Barycentric Subdivision
part 7: Week 7
session 33: Lecture 33 : Finer Subdivisions
session 34: Lecture 34 : Simplical Approximation
session 35: Lecture 35 : Sperner Lemma
session 36: Lecture 36 : Invariance of domain
session 37: Lecture 37 : Proof of controled homotopy
part 8: Week 8
session 38: Lecture 38 : Links and Stars
session 39: Lecture 39 : Homotopical Aspects of Simplicial Complexes
session 40: Lecture 40 : Homotopical Aspects
session 41: Lecture 41 : Covering Spaces and Fund. Groups
session 42: Lecture 42 : Lifting Properties
part 9: Week 9
session 43: Lecture 43 : Homotopy Lifting
session 44: Lecture 44 : Relation with the fund. Group
session 45: Lecture 45 : Regular covering
session 46: Lecture 46 : Lifting Problem
session 47: Lecture 47 : Classification of Coverings
part 10: Week 10
session 48: Lecture 48 : Classification
session 49: Lecture 49 : Existence of Simply connected coverings
session 50: Lecture 50 : Construction of Simply connected covering
session 51: Lecture 51 : Properties Shared by total space and base
session 52: Lecture 52 : Examples
part 11: Week 11
session 53: Lecture 53 : G-coverings
session 54: Lecture 54 : Pull-backs
session 55: Week 11 : Lecture 55
session 56: Lecture 56 : Proof of classification
session 57: Lecture 57 : Pushouts and Free products
part 12: Week 12
session 58: Lecture 58 : Existence of Free Products, pushouts
session 59: Lecture 59 : Free Products and free groups
session 60: Lecture 60 : Seifert-Van Kampen Theorems
session 61: Lecture 61 : Applications
session 62: Lecture 62 : Applications continued
part 13: Live Session
session 63: Live Session 05-02-2021
session 64: Live Session 24-02-2021
session 65: Live Session 19-03-2021

Catalogue records

nptel: 111101144 (manifestation)
nptel_video: 111101144 (manifestation)