Differential Topology | Lecture 2 by John W. Milnor

Soon after winning the Fields Medal in 1962, a young John Milnor gave these now-famous lectures and wrote his timeless Topology from the Differentiable Viewpoint -www.mat.unimi.it/users/dedo/to... , which has influenced generations of mathematicians. The lectures, filmed by the Mathematical Association of America (MAA), were unavailable for years but recently resurfaced. With Simons Foundation funding, the Mathematical Sciences Research Institute has produced these digital reproductions as a resource for the mathematics and science communities.
Milnor was awarded the Abel Prize in 2011 for his work in topology, geometry and algebra.
The sequel to these lectures, written several mathematical lives - and a Wolf and an Abel Prize later - is "Differential Topology Forty-six Years Later,"- www.ams.org/notices/201106/rtx...
Source of the above information and lecture: www.simonsfoundation.org/scie...
Also quite helpful:
Differential Topology
Lectures by John Milnor, Princeton University, Fall term 1958
Notes by James Munkres - www.maths.ed.ac.uk/~aar/papers...

[@user-lt9vw3ry4x]

It's great information american

[@angelseye7492]

John Milnor is whom academic society hope, truly achievement.

[@Mathview]

Outstanding post! Before my time at Cornell, but I had heard stories of this legendary lecture series for the non-specialist, now this is my first opportunity to see them here on KZbin. TY for posting.

[@wither8]

Why does the lemma @34:00 only hold for the piecewise linear and topological cases, but not for the differential category?

[@BehnamEsmayli]

Because at origin, the function won't be differentiable. It will be torn apart by all directions.

[@gylje-9905]

at 21:09 when characterizing the disk, how can its boundary be simply connected? Its not in n=2.(Which in that situation is a circle)

[@xXUxCXx]

It's simply connected for all dimensions greater than two

[@BehnamEsmayli]

At kzbin.info/www/bejne/maGZlqiaedSgiLs didn't he just say that for n>6 the topological case will be isomorphic to the usual sphere? But then earlier he'd said that we don't know anything about top P.C. for n>2! ANY HELP?

[@vallikalli]

The earlier topological case was concerning an arbitrary set in a topological space, iirc

[@MrBorest]

I have the impression that lectures at this time were way more pedrestian than nowdays