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

Lecture 4

This Lecture is about

1. Quotient in topology
   1. using cut to understanding quotient
2. Introduction to $\Sigma g$ and $Ng$
3. Homeomorphism

Lecture 5

This Lecture is about

1. The transformation between $\Sigma g$ and $Ng$
2. Overflow
3. The L dimension object vs K dimension object in M dimension

Lecture 6

This Lecture is about

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

Lecture 7

This Lecture is about

1. The positive and negative intersection
   1. There is no tangent [vector] intersection in Topology
2. Intersect transversely

Lecture 8

This Lecture is about

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

Lecture 15

This Lecture is about

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

Some interesting websites that referred to this lecture series.