Covering spaces | Algebraic Topology | NJ Wildberger

[@HDQuote]

NJ wildberger, you are an amazing teacher! You make my courses in algebraic topology sooo much more fun! Not just that, but you are a great teacher in general! The world benefits a lot from your works!

[@njwildberger]

Yes, a trefoil knot is certainly homeomorphic to a circle: in fact any knot is. When we discuss knot theory we study how a particular circle is embedded in three dimensional space. So it is the relationship between the circle and the ambient space that is important.

[@hellenakinyi7942]

Video Content 00:00 Introduction 00:55 Homomorphisms of fundamental groups 08:09 Covering space 21:20 Def p X --> B in a covering map if 24:40 Example 2 on images 29:29 Example 3 on images 33:30 Algebraic interpretation 36:47 Another physical model of the helical covering of a circle uses a torus - Torus knots 47:10 Example p S¹-> S¹×S¹ t-> ( 2+,3+) mod 1 50:13 Making a diagram of a torus and a trefoil knot 52:45 Problem; Describe the torus knot associated to S¹->S¹×S¹ t->(3t,4t) mod 1

[@smithsonian2516]

sir, your lectures are one of the best available online or otherwise as well

[@WildEggmathematicscourses]

Thanks Prabhakar. If you would like to support the channel, we do have a Patreon page--from which you can then access the online Algebraic Calculus One course which is very exciting!

[@njwildberger]

Yes you are right, that cover that I said was 3:1 was actually 4:1. Thanks.

[@barteqw]

Excellent explained. At the moment i'm reading Czes Kosniowski book to Algebraic Topology, i like your way of teaching, really helpful. Best regards from Poland.

[@salvatoregiordano6816]

Beautiful teaching! Very engaging and clear

[@jackozeehakkjuz]

Ah... such a wonderful appearence of the fundamental group(oid) functor. I almost thought you were gonna start talking about categories haha.

[@turiskikinai9689]

Amir, if you're interested, he's quite clearly detailed his viewpoint in other videos, you need only look his name up on google to find them. But the crux of the matter is explained in MF42a: ( MF42a: Deflating modern mathematics: the problem with `functions' ) where he shows that the modern conception of functions is flawed. You can scroll through the rest of the series and find the obviously relevant videos; fair warning, you will probably not want to watch all of them in one sitting: some are quite long.

[@njwildberger]

Your question is logically incoherent, since you are assuming the existence of R.

[@HotPepperLala]

p(-3 1/3) = 1/3 mod 1

[@md2perpe]

He's a realnumberphobic. ;-)

[@njwildberger]

For a very good reason: the theory of ``real numbers'' is a fraud.