Learn · Introduction to Algebraic Topology (Part-II)
Lecture 50 of 62week-10
Week 10-Lecture 48 : Manifolds with Boundary
Prof. Anant R. Shastri · IIT Bombay
Credits and licence
- From
- Introduction to Algebraic Topology (Part-II), IIT Bombay (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Week 1-Lecture 1 : Introduction
- Week 1-Lecture 2 : Attaching cells
- Week 1-Lecture 3 : Subcomplexes and Examples
- Week 1-Lecture 4A : More examples
- Week 1-Lecture 4B : More Examples
- Weeek 1-Lecture 5 : Topological Properties
- Week 2-Lecture 6 : Coinduced Topology
- Week 2-Lecture 7 : Compactly generated topology on Products
- Week 2-Lecture 8 : Product of Cell complexes
- Week 2-Lecture 9 : Product of Cell complexes-Continued
- Week 2-Lecture 10 : Partition of Unity on CW-complexes
- Week 3-Lecture 11 : Partition of Unity-Continued
- Week 3-Lecture 12 : Homotopical Aspects
- Week 3-Lecture 13 : Homotopical Aspects-Continued
- Week 3-Lecture 14 : Cellular Maps
- Week 3-Lecture 15 : Cellular Maps-Continued
- Week 4-Lecture 16A : Homotopy exact sequence of a pair
- Week 4-Lecture 16B : Homotopy exact sequence of a fibration
- Week 4-Lecture 17 : Categories-Definitions and Examples
- Week 4-Lecture 18 : More Examples
- Week 4-Lecture 19 : Functors
- Week 4-Lecture 20 : Equivalence of Functors-Continued
- Week 5-Lecture 21 : Universal Objects
- Week 5-Lecture 22 : Basic Homological Algebra
- Week 5-Lecture 23 : Diagram-Chasing
- Week 5-Lecture 24 : Homology of Chain Complexes
- Week 5-Lecture 25 : Euler Characteristics
- Week 6-Lecture 26 : Singular Homology Groups
- Week 6-Lecture 27 : Basic Properties of Singular Homology
- Week 6-Lecture 28 : Excision
- Week 6-Lecture 29 : Examples of Excision-Mayer Vietoris
- Week 6-Lecture 30 : Applications
- Week 7-Lecture 31 : Applications-Continued
- Week 7-Lecture 32 : The Singular Simplicial Homology
- Week 7-Lecture 33 : Simplicial Homology
- Week 7-Lecture 34 : Simplicial Homology-Continued
- Week 7-Lecture 35 : CW-Homology and Cellular Singular Homology
- Week 8-Lecture 36 : Construction of CW-chain complex
- Week 8-Lecture 37 : CW structure and CW homology of Lens Spaces
- Week 8-Lecture 38 : Assorted Topics
- Week 8-Lecture 39 : Some Applications of Homology
- Week 8-Lecture 40 : Applications of LFT
- Week 9-Lecture 41 : Jordan-Brouwer
- Week 9-Lecture 42 : Proof of Lemmas
- Week 9-Lecture 43 : Relation between ?1 and H1
- Week 9-Lecture 44 : All Postponed Proofs
- Week 9-Lecture 45 : Proofs-Continued
- Week 10-Lecture 46 : Definitions and Examples
- Week 10-Lecture 47 : Paracompactness
- Week 10-Lecture 48 : Manifolds with Boundary
- Week 10-Lecture 49 : Embeddings and Homotopical Aspects
- Week 10-Lecture 50 : Homotopical Aspects continued
- Week 11-Lecture 51 : Classification of 1-manifolds
- Week 11-Lecture 52 : Classification of 1-manifolds-continued
- Week 11-Lecture 53 : Triangulation of Manifolds
- Week 11-Lecture 54 : Pseudo-Manifolds
- Week 11-Lecture 55 : One result due to Poincaŕe and another due to Munkres
- Week 12-Lecture 56 : Some General Remarks
- Week 12-Lecture 57 : Classification of Compact Surface
- Week 12-Lecture 58 : Final Reduction-Completion of the Proof
- Week 12-Lecture 59 : Proof of Part B
- Week 12-Lecture 60 : Orientability