Topology and Geometry

Introduction to Topology and Geometry

This is a course that Henry and Ben are studying during 2021.

content

1. Lecture 1
2. Lecture 2
   1. Solving problem by deformation
   2. Understanding by turning it to a higher dimension
   3. Introduction to Basic Building Blocks of Topology and Geometry
      1. n-ball $B^{n}$
      2. (n-1)-sphere $S^{n},n-1$ (Don't know why I can't write the )
      3. what is the different between circle and disk
3. Lecture 3
   1. The Operation of I:product
      1. m-cube $I^{m}$
   2. m-torus $T^{m}$
   3. The multiplication of shape in Topology and Geometry
   4. Quotient in topology
      1. all kinds of quotient example
      2. using cut to understanding quotient
4. Lecture 4
   1. Quotient in topology
      1. using cut to understanding quotient
   2. Introduction to $\Sigma g$ and $Ng$
   3. Homeomorphism
5. Lecture 5
   1. The transformation between $\Sigma g$ and $Ng$
   2. Overflow
   3. The L dimension object vs K dimension object in M dimension
6. Lecture 6
   1. Isotopic
   2. The relationship between isotopic and homeomorphic
   3. outside the shape inside the shape
   4. The positive and negative intersection
      1. There is no tangent vector intersection in Topology
7. Lecture 7
   1. The positive and negative intersection
      1. There is no tangent [vector] intersection in Topology
   2. Intersect transversely
8. Lecture 8
   1. Jordan curve theorem
      1. If you have a closed curve which does not intersect itself it will divide the plan into two parts.
   2. Fixed Point Theorem
9. Lecture 9
10. Lecture 10
11. Lecture 11
12. Lecture 12
13. Lecture 13
14. Lecture 14
15. Lecture 15

Also, we should make proper reference, and it will show at the Reference section.

Some interesting websites that referred to this lecture series.