Introduction to the fundamental group

A leisurely introduction to the idea of homotopy, including a sketch proof that the fundamental group of the circle is the integers. This is aimed at second year undergrads embarking on projects in geometry/topology who need to quickly learn the basic idea of the fundamental group, so the focus is on developing intuition and explaining the definitions.

[@juaniribasdelapuerta9535]

I regret no having seen this video before my Topology course got started, it's really eye-opening, thank you very much

[@asthaverma366]

Where is it's full playlist... I didn't find this vdo on the topology playlist..

[@ceciliasaraivaunirio]

Congratulations! You are an excellent professor. Your explanation is simple and correct. Really cool!

[@sadface7457]

Been looking for a nice calming math video.

[@mohamedradwan388]

Excellent. Thanks !

[@meruhere]

Hey thanks for the video! I recently read Homotopy in Mendelson's Introduction to Topology, and this video helped in grasping the "math" in whole of the discussion and abstraction of paths and connectedness.

[@gregoriousmaths266]

abhineet sharma I’ve read that book and a recommendation I would have if ur interested is algebraic topology by Allen hatcher

[@holographictheory1501]

A literal life saver, thank you!

[@pupnoomann7866]

omg i can't believe they would have killed you for failing

[@asthaverma366]

Great content😊

[@endlessentropy9107]

Awesome!

[@bishop1640]

Very very helpful thank you

[@bradleygaddis5155]

The fundamental group is a homotopy to the diagonal entries ( one fundamental group for each diagonal entry) in the subroutine call from-to matrix via Warshalls algorithm. The diagonal entry indicates if a subroutine ever calls itself(loops back to itself)!!!
Clue: cf AI networks and how this applies!!!

[@JosiahWarren]

Thank you so much. Please support also the Homotopy type book if you are computer scientist

[@omargaber3122]

Does this help with number theory?!! How can it be used?! For example, if I wanted to prove Fermat's Last theorem, how could it be used?

[@samtux762]

What field is this? Topology? Group theory?

[@rfabbri]

"it's called the Pochhammer contour"

[@bobjoe7380]

Thank you, unfortunately my professor is not the best explainer in the world ;)

[@medamin3333]

c est quoi embedding en francais slp merci d avance

[@jonathanevans27]

"Plongement", n'est pas?

[@medamin3333]

@@jonathanevans27 je ne sais pas tu es sûr ?