Difference between revisions of "Topology and Geometry"
Jump to navigation
Jump to search
Line 25: | Line 25: | ||
## Introduction to <math> \Sigma g </math> and <math> Ng </math> | ## Introduction to <math> \Sigma g </math> and <math> Ng </math> | ||
## [[Homeomorphism]] | ## [[Homeomorphism]] | ||
#[[Lecture:Topology and Geometry 5|Lecture 5]] | #[[Lecture:Topology and Geometry 5|Lecture 5]] | ||
##The transformation between <math> \Sigma g </math> and <math> Ng </math> | ##The transformation between <math> \Sigma g </math> and <math> Ng </math> |
Revision as of 05:21, 22 July 2021
Introduction to Topology and Geometry
This is a course that Henry and Ben are studying during 2021.
content
- Lecture 1
- Lecture 2
- Solving problem by deformation
- Understanding by turning it to a higher dimension
- Introduction to Basic Building Blocks of Topology and Geometry
- n-ball
- (n-1)-sphere (Don't know why I can't write the )
- what is the different between circle and disk
- Lecture 3
- The Operation of I:product
- m-cube
- m-torus
- The multiplication of shape in Topology and Geometry
- Quotient in topology
- all kinds of quotient example
- using cut to understanding quotient
- The Operation of I:product
- Lecture 4
- Quotient in topology
- using cut to understanding quotient
- Introduction to and
- Homeomorphism
- Quotient in topology
- Lecture 5
- The transformation between and
- Overflow
- The L dimension object vs K dimension object in M dimension
Lecture 6
This Lecture is about
- Isotopic
- The relationship between isotopic and homeomorphic
- outside the shape inside the shape
- The positive and negative intersection
- There is no tangent vector intersection in Topology
Lecture 7
This Lecture is about
- The positive and negative intersection
- There is no tangent [vector] intersection in Topology
- Intersect transversely
Lecture 8
This Lecture is about
- Jordan curve theorem
- If you have a closed curve which does not intersect itself it will divide the plan into two parts.
- Fixed Point Theorem
Lecture 9
This Lecture is about
Lecture 10
This Lecture is about
Lecture 11
This Lecture is about
Lecture 12
This Lecture is about
Lecture 13
This Lecture is about
Lecture 14
This Lecture is about
Lecture 15
This Lecture is about
Also, we should make proper reference[1], and it will show at the Reference section.
Some interesting websites[2] that referred to this lecture series.
References
- ↑ Tokieda, Tadashi (12 May 2014). Topology and Geometry. 3/15. African Institute of Mathematical Sciences.
- ↑ Gaurish, Gaurish4Math on Topology ,https://gaurish4math.wordpress.com/tag/tadashi-tokieda/, last accessed: July 22, 2021