NOC:Introduction to Algebraic Topology - Part II

Lecture 1 - Introduction

Lecture 2 - Attaching cells

Lecture 3 - Subcomplexes and Examples

Lecture 4 - More examples

Lecture 5 - More Examples

Lecture 6 - Topological Properties

Lecture 7 - Coinduced Topology

Lecture 8 - Compactly generated topology on Products

Lecture 9 - Product of Cell complexes

Lecture 10 - Product of Cell complexes (Continued...)

Lecture 11 - Partition of Unity on CW-complexes

Lecture 12 - Partition of Unity (Continued...)

Lecture 13 - Homotopical Aspects

Lecture 14 - Homotopical Aspects (Continued...)

Lecture 15 - Cellular Maps

Lecture 16 - Cellular Maps (Continued...)

Lecture 17 - Homotopy exact sequence of a pair

Lecture 18 - Homotopy exact sequence of a fibration

Lecture 19 - Categories-Definitions and Examples

Lecture 20 - More Examples

Lecture 21 - Functors

Lecture 22 - Equivalence of Functors (Continued...)

Lecture 23 - Universal Objects

Lecture 24 - Basic Homological Algebra

Lecture 25 - Diagram-Chasing

Lecture 26 - Homology of Chain Complexes

Lecture 27 - Euler Characteristics

Lecture 28 - Singular Homology Groups

Lecture 29 - Basic Properties of Singular Homology

Lecture 30 - Excision

Lecture 31 - Examples of Excision-Mayer Vietoris

Lecture 32 - Applications

Lecture 33 - Applications (Continued...)

Lecture 34 - The Singular Simplicial Homology

Lecture 35 - Simplicial Homology

Lecture 36 - Simplicial Homology (Continued...)

Lecture 37 - CW-Homology and Cellular Singular Homology

Lecture 38 - Construction of CW-chain complex

Lecture 39 - CW structure and CW homology of Lens Spaces

Lecture 40 - Assorted Topics

Lecture 41 - Some Applications of Homology

Lecture 42 - Applications of LFT

Lecture 43 - Jordan-Brouwer

Lecture 44 - Proof of Lemmas

Lecture 45 - Relation between ?1 and H1

Lecture 46 - All Postponed Proofs

Lecture 47 - Proofs (Continued...)

Lecture 48 - Definitions and Examples

Lecture 49 - Paracompactness

Lecture 50 - Manifolds with Boundary

Lecture 51 - Embeddings and Homotopical Aspects

Lecture 52 - Homotopical Aspects (Continued...)

Lecture 53 - Classification of 1-manifolds

Lecture 54 - Classification of 1-manifolds (Continued...)

Lecture 55 - Triangulation of Manifolds

Lecture 56 - Pseudo-Manifolds

Lecture 57 - One result due to Poincaŕe and another due to Munkres

Lecture 58 - Some General Remarks

Lecture 59 - Classification of Compact Surface

Lecture 60 - Final Reduction-Completion of the Proof

Lecture 61 - Proof of Part B

Lecture 62 - Orientability