If g is a group element, then g^n=g*g*...*g (n times). So if g is a transformation, then g^n is the n fold repetition of g, if the multiplication we are considering is composition.
First of all: this series on algebraic topology is really great. At the time I attended college I didn't really took (or had) the opportunity to take many extra curriculair math-courses but this subject did draw my attention because of the fact that the course in advanced calculus, which I attended, contained references to metric topologies and topology in general. In this manner I can catch up with some things that I more-or-less missed out on: thank you professor Wildberger for making this available! I actually ended up here by first viewing the 'Insight into Mathematics' series on the history of mathematics. Secondly I have a question about the genus of the 2-holed torus that is mentioned around 26:00 in the UA-cam-clip at hand: aren't the two cuts that are presented the same/similar because they're topologically indistinguishable? How does a cut between the two loops fit into this picture? A cut like that doesn't actually separate the torus but can or may basically change it into a single holed torus. Anyone?
Okay, after a little contemplation I got my head around this; ofcourse it's easier than I thought (as always). Making one cut around the double torus (a 'circumferential cut' so to say) always projects it onto the equivalence class of the single torus, be it a cut between the loops or not. A second 'circumferential cut' then always projects the object onto the equivalence class of the sphere. Got it.
Thank you from a Czech guy - your lectures are amazing. ilkhamharzmiy - I bet I will have to visit Uzbekistan at some point then, as I have been enjoying living in Czech Republic very much so far :).
Hi, professor,Wilberger thanks for your priceless courses and benevolent sharing of knowledge is there any book or more precisely is there any theory about calculating the surface area of topological structures like Seifert surface or n holed Toroses like the way we integrate the area under a curve
Hi Mr.Wildberger, thanks for the channel firstly. I love the job you're doing. I'm hoping to learn all the courses you've put up. Btw can you provide the solution for the problems you're posting? Particularly the clothesline with the 2 hole torus problem
Problem 8 solution: math.stackexchange.com/questions/107782/continuously-deform-2-torus-with-a-line-through-one-hole-to-make-it-go-through-b
The example at 29:30 is such a revelation for me! Thank you so much for sharing this wonderful series, Prof Wildberger!
Thankyou. Dr. Wildberger
If g is a group element, then g^n=g*g*...*g (n times). So if g is a transformation, then g^n is the n fold repetition of g, if the multiplication we are considering is composition.
What are the best aspects of life there? (I realize this doesn't have much to do with Alg Top, but its interesting for me anyway)
well said, professor!!!
Thankyou
First of all: this series on algebraic topology is really great. At the time I attended college I didn't really took (or had) the opportunity to take many extra curriculair math-courses but this subject did draw my attention because of the fact that the course in advanced calculus, which I attended, contained references to metric topologies and topology in general. In this manner I can catch up with some things that I more-or-less missed out on: thank you professor Wildberger for making this available!
I actually ended up here by first viewing the 'Insight into Mathematics' series on the history of mathematics.
Secondly I have a question about the genus of the 2-holed torus that is mentioned around 26:00 in the UA-cam-clip at hand: aren't the two cuts that are presented the same/similar because they're topologically indistinguishable? How does a cut between the two loops fit into this picture? A cut like that doesn't actually separate the torus but can or may basically change it into a single holed torus. Anyone?
Okay, after a little contemplation I got my head around this; ofcourse it's easier than I thought (as always). Making one cut around the double torus (a 'circumferential cut' so to say) always projects it onto the equivalence class of the single torus, be it a cut between the loops or not. A second 'circumferential cut' then always projects the object onto the equivalence class of the sphere.
Got it.
Thank you professor , have been studying this subject on my own this video series helped a lot !!
Thank you from a Czech guy - your lectures are amazing. ilkhamharzmiy - I bet I will have to visit Uzbekistan at some point then, as I have been enjoying living in Czech Republic very much so far :).
Nice to hear from you. Are you living in Uzbekistan? If so, is it easy to get a good UA-cam reception there? (Sorry if that's a silly question).
Hi, professor,Wilberger
thanks for your priceless courses and benevolent sharing of knowledge
is there any book or more precisely is there any theory about calculating the surface area of topological structures like Seifert surface or n holed Toroses
like the way we integrate the area under a curve
Hi Mr.Wildberger, thanks for the channel firstly. I love the job you're doing. I'm hoping to learn all the courses you've put up. Btw can you provide the solution for the problems you're posting? Particularly the clothesline with the 2 hole torus problem
nice lecture/lesson. thanks for the info
thank you very much from an uzbek guy!!!
Thankyou.
Thankyou
Thankyou