Algebraic Topology 9 : Deck Transformations of Covering Spaces

We complete our study of covering spaces by discussing the group of deck transformations of a covering space, that is, the group formed by isomorphisms from a covering space to itself that send basepoints to basepoints. We see that this group is the quotient of the fundamental group of the base space and that of the covering space, at least when the covering space is normal (i.e. symmetric). We see several examples of this. Then we wrap up with a brief introduction of Geometric Group Theory by discussing how to construct the Cayley graph of a group.

Presented by Anthony Bosman, PhD.

[xanderlewis]

I feel like 'so... DO IT!' is your catchphrase. I love it. These lectures do skirt over some formalities (although that's what books are for anyway) but they're an absolutely fantastic thing to watch to build intuition and refresh one's knowledge. Teaching is an underrated skill, and you're clearly brilliant at it. I'm having so much fun watching these and following along.

[timelsen]

Wonderful Presentation. Best ever for my self taught efforts, in rounding out my understanding of several topics all at once!

[hyperduality]

Deck transformations are dual to permutations.
Rotations are dual to reflections.
Symmetry is dual to anti-symmetry -- permutation groups.
"Always two there are" -- Yoda.
Subgroups are dual to subfields -- the Galois correspondence.

[GunsExplosivesnStuff]

This helped me in my life. You have earned a subscriber :)

[AhmadKhan-spqb]

great lectures! what semester is this being taught to? also, what do you think about the book introduction to topological manifolds by john M lee for algebraic topology?

[depressedguy]

Amazing, every Thursday one episode is coming, are you taking one class per week in your university.

[-minushyphentwo]

29:30 Group of homeomorphisms of covering space preserving image of each point and orientation of curve(??? I don’t get why the orientation is preserved) is isomorphic to quotient group of fundamental group of base space by fundamental group of covering space

[ompatel]

32:24 can you please explain this a little bit better