MWF 11:30–12:30 in ES-153.
AMAT 520 & 540, or permission of instructor.
The ultimate goal of this course is to present a proof of the celebrated s-cobordism theorem, from which a proof of the Poicaré conjecture in dimensions 5 or more easily follows. These are some of the most important breakthroughs in geometric topology of the last half century. Along the way we will learn, among other things, about smooth manifolds with or without boundary, Morse theory, handle decompositions, surgery, Whitehead torsion, and the first algebraic K-theory group of a ring.
None, but the following lecture notes, which are freely available online, are an excellent reference.
Wolfgang Lück, A basic introduction to surgery theory, in Topology of high-dimensional manifolds, Vol. 1, 1–224, ICTP Lect. Notes 9, Trieste, 2002.
And the following textbook, which has recently been reprinted by Dover Publications and can be bought for about $10, is also worth recommending.
- Antoni A. Kosinski, Differential Manifolds, Dover, 2007.
Biweekly homework assignments.