GEOMETRY
TOPOLOGY SEMINAR

“Dolgachev
Surfaces”

by

Prof. selman Akbulut

(Michigan State universıty)

Abstract: Are there exotic
copies of S^4 or CP^2 ? It is known that if they exist
they must contain 1- or 3-handles. About 25 years ago Donaldson gave the first
example of an exotic orientable smooth 4-manifold, i.e. he proved that
Dolgachev&#8217;s complex surface E(1)2,3 is an
exotic copy of CP^2 #9(&#8722;CP^2); about the same time Harer Kas and
Kirby wrote a book about E(1)2,3 where they conjectured that it must contain 1-
or 3-handles. We will discuss the recent solution of this conjecture (in the
negative). In this context we will relate the proof to &#8221;corks&#8221; and &#8221;plugs&#8221;, which are
roughly freely floating particles in 4-manifolds determining their exotic
structures.

Date : December 20, 2010 (Monday)

Time : 13.40-14.30

Place: Bilkent University,Mathematics
Seminar Room SA-141