University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

AMAT 587: Topics in Modern Mathematics, Manifold Topology, Fall 2012


Prof. Marco Varisco,,
Office: ES-120C, Office Hours: MWF 8:15–9:15, or by appointment.


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.

And the following textbook, which has recently been reprinted by Dover Publications and can be bought for about $10, is also worth recommending.


Biweekly homework assignments.

This syllabus is subject to change. All official announcements and assignments are given in class, and this web page may not be up to date.
Marco Varisco.