NOC:Introduction to Algebraic Topology - Part I

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...)