© 2008 London Mathematical Society
Constructing infinitely many smooth structures on small 4-manifolds
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA ahmadov@math.gatech.edu
nanç Baykur
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Current address: Department of Mathematics, Columbia University, New York, NY 10027, USA baykur@math.columbia.edu
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada bdpark@math.uwaterloo.ca
The purpose of this article is two-fold. First we outline a general construction scheme for producing simply connected minimal symplectic -manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain irreducible symplectic -manifolds homeomorphic but not diffeomorphic to 
for k = 1, ..., 4, or to 
for l = 1, ..., 6. Secondly, for each of these homeomorphism types, we show how to produce an infinite family of pairwise nondiffeomorphic nonsymplectic 4-manifolds belonging to it. In particular, we prove that there are infinitely many exotic irreducible nonsymplectic smooth structures on, 
and 
.
Received April 17, 2007. Revised September 26, 2007.
2000 Mathematics Subject Classification 57R55, 57R57
A. Akhmedov was partially supported by NSF grant FRG-0244663, R. . Baykur was partially supported by NSF Grant DMS-0305818, and B. D. Park was partially supported by CFI, NSERC and OIT grants.
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