Algebraic Topology 1.1 : Homotopy (Animation Included)

In this video, I will introduce homotopy equivalence, some basic examples of homotopy, and the transitivity of homotopy. I use an animation to intuitively explain these concepts.

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[duckymomo]

Yay I love studying Algebraic Topology, this will be a fun series

[kunjaai]

What a nice and simple way of presentation .. .. really liked and thanks for the lecture <3

[jonathannissim]

Really helped me understand this, thanks!

[arturo]

Hello sir, 0 is a point in R not R2. Shouldn't H map to (0, , 0) ?

[kaushikdr]

Shouldn't the full H(x, t) = f(x)(1-t) + g(x)(t)? Also, I got what you mean when you said two curves were homotopic, but I was hit with a curveball when you said "homotopic to 0" - what does this mean? How can you make a curve go to a number? If you mean that a shape can be "shrunk down to a point", can't you also say "homotopic to {}".format(any real number)? (Haha I thought I would use some Python notation ;D)

[duckymomo]

H(x, t) = (1-t)•f(x)

How did you determine that 1 constant? Is it from the end point of t = [0, 1]? Will it usually be in this form or is it the homotopy that works for this particular relation?

[duckymomo]

Is a homotopy unique?

How do we know such a homotopy exists?

[TheNachoesuncapo]

what do you do during math class at school?

[farukahmed]

I loved this video. Love from India....

[antoinevince]

is it possible to define homotopy between algebraic variety ?

[umergulzar]

I need help with some questions can u help

[chandankar]

Can you recommend a book for beginning algebric topology ?

[isleofdeath]

What if the space [0, 1] x X is not convex?

[existenceispain]

show that homeomorphic doesn't imply homotopic