 
Summary: arXiv:0906.3107v1[math.GT]17Jun2009
AN INFINITE FAMILY OF EXOTIC DOLGACHEV
SURFACES WITHOUT 1 AND 3 HANDLES
SELMAN AKBULUT
Abstract. Starting with the Dolgachev surface E(1)2,3 we con
struct an infinite family of distinct exotic copies of the rational
surface E(1), each of which admits a handlebody decomposition
without 1 and 3 handles, and we draw these handlebodies.
0. Introduction
It is an old problem to determine when an exotic copy of a smooth
simply connected 4manifold admits a handle decomposition without
1 and 3 handles. Note that if an exotic S4
or CP2
exists then its han
dle decomposition must contain either 1 or 3handles. Finding such
exotic manifolds realizing the smallest Betti number is particularly an
interesting problem. For example in [Y] and also [AY] exotic manifolds
without 1 and 3 handles were demonstrated. An interesting difficult
case has been the Dolgachev surface E(1)2,3, which is an exotic copy of
E(1) = CP2
