Path in Space to fundamental group
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users point people to it for its clear square diagram of a homotopy and its proof that inverses exist in the fundamental group.
Recommended by 2 people across 2 different months, 2019 to 2023.
What it is
A lecture by Harpreet Bedi building the fundamental group from paths in a topological space. It covers path homotopy, how to picture a homotopy as a map on the unit square in s and t, and the existence of inverses for loops.
What people said
Recommends user965463 · 2023-02 · Mathematics Stack Exchange · on “Understanding the explicit homotopy of Exercise 1.1.10”
if you look at this video on min 14 you will understand what I wanna say [this video] I am asking in our case here is s and t ranging also from 0 to 1?
Recommends Intuition · 2023-03 · Mathematics Stack Exchange · on “Describing the homotopy explicitly.”
I mean how did you construct your homotopy? people usually draw a square with t as the horizontal (x - coordinate ) and s as the vertical (y - coordinate) and express the homotopy in terms of this ........... you can use quiver [LINK] on your laptop, I will edit my post to include an example of a picture of a homotopy like in Harpreet Bedi video "Path in space to fundamental group" [this video] min. 6
Cites user591668 · 2019-07 · Mathematics Stack Exchange · on “The difference between proving the existence of the inverse of the fundamental group between a book and a youtube lecture.”
The following lecture proof the existence of the inverse for the fundamental group starting from minuite 15: [this video] But "Introduction to knot theory book" of Richard H. Crowell, prove it as follows: [LINK] [LINK] [LINK] [LINK] But I want to transform the homotopy given in the book to what given on youtube, because what is given in the book is not clear for me, could anyone help me in doing so please?