The Poincare Conjecture in dimension 2, or why topologists can’t tell their donuts from their cups of coffee

Posted on: March 6, 2017

Math Club Talk

Jeanne Clelland, University of Colorado

“The Poincare Conjecture in dimension 2, or why topologists can’t tell their donuts from their cups of coffee”

Thursday, 3/30/17 at 4pm

Manchester 016

Abstract:  In 2006, Grigori Perelman declined to accept a Fields medal (often referred to as the “Nobel Prize for mathematics”) for his proof of the Poincare conjecture, one of the most important unsolved problems in mathematics.  Loosely speaking, this conjecture says, “If it looks like a 3-sphere, then it is a 3-sphere.”  Oddly, the analog of this result was first proved for spheres of dimension 5 and greater in the mid-1960’s, then for spheres of dimension 4 in the 1980’s, and dimension 3 was the last open case.
I will try to convey a sense of what all the fuss is about, and then we will explore the much simpler case of compact 2-dimensional surfaces, where the complete classification is fairly simple and has been well-understood since the early 20th century.
No prior knowledge is assumed, although having played with Silly Putty as a child might be helpful.