AlgTop23: Knots and surfaces II

In the 1930's H. Siefert showed that any knot can be viewed as the boundary of an orientable surface with boundary, and gave a relatively simple procedure for explicitly constructing such `Seifert surfaces'. We show the algorithm, exhibit it for the trefoil and the square knot, and then discuss Euler numbers for surfaces with boundaries.

This is part of a beginner's course on Algebraic Topology given by N J Wildberger of the School of Mathematics and Statistics, UNSW.

[chosop]

Wow, I never understood this before. So clear and understandable! Thanks so much.

[leokyere]

This Lecture is very intuitive. I enjoyed every second and every micro-second of it

[kitefrog]

I've discovered, that when you cut the 3-flip mobius strip down the middle, let it make 6 natural crossing when it wants to do, let the boundary cross itself to get a framed knot. Then draw the family of knot diagrams. The Jones Polynomail of the Mobius Knots equals the Jones Polynomial of the 3 band Siefert Surface when it is also cut down the middle avoiding the center of the disks. It also requires 6 crossings to make a frames knot and cancel the 8 twists. why is that? See my videos

[alfredorestrepo]

Herbert Seifert was a German mathematician.