What is...homotopy of spheres?

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Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.

This time.
What is...homotopy of spheres? Or: Surprisingly hard!?

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.

Thumbnail.

Main discussion.

Mathoverflow likes this topic.

Mathematica.

Pictures used.

YouTube and co.

#algebraictopology
#topology
#mathematics
  1. VisualMath
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Комментарии
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I remember a generalized version of Van Kampen’s theorem and crossed modules being using when working with higher homotopy groups.

Jaylooker
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This is an excellent video 👍👍
Thank you processor.

I liked the 'pant' analogy that you gave in the other video. Your videos are helping many people who are studying.

You have an excellent way of giving explanation. Moreover, this channel contains very important videos in Topology.

Thank you again 💕💕

asiancollegeofteachers
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It would be nice if homotopy groups of n-spheres formed an upper/lower triangle matrix excluding S_0. I think this has do with to with stable homotopy theory which explains the diagonal Z entries. Looking into the J-Homomorphism and Bott Periodicity or similar ideas may also help explain how numbers multiple of 12 appears in the matrix.

Jaylooker
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