NOC:Introduction to Algebraic Topology - Part II

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 : 6.5 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

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