 
Summary: TWISTING 4MANIFOLDS ALONG RP2
SELMAN AKBULUT
Abstract. We prove that the Dolgachev surface E(1)2,3 (which
is an exotic copy of the elliptic surface E(1) = CP2
#9 ¯CP
2
) can be
obtained from E(1) by twisting along a simple "plug", in particular
it can be obtained from E(1) by twisting along RP2
.
0. Introduction
Given a smooth 4manifold M4
, what is the minimal genus g of
an imbedded surface g M4
, such that twisting M along pro
duces an exotic copy of M? Here twisting means cutting out a tubular
neighborhood of and regluing back by a nontrivial diffeomorphism.
Not much known about the case g > 1. The case g = 1 is the well
known"logarithmic transform" operation, which can change the smooth
structure in some cases; in fact the first example of a closed exotic man
