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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The geography of symplectic $ 4$-manifolds with an arbitrary fundamental group


Author: Jongil Park
Journal: Proc. Amer. Math. Soc. 135 (2007), 2301-2307
MSC (2000): Primary 57R17, 57R57; Secondary 57N13
Published electronically: March 2, 2007
MathSciNet review: 2299508
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Abstract: In this article, for each finitely presented group $ G$, we construct a family of minimal symplectic $ 4$-manifolds with $ \pi_1 =G$ which cover most lattice points $ (x, {\mathbf c})$ with $ x$ large in the region $ 0 \leq {\mathbf c} < 9x$. Furthermore, we show that all these $ 4$-manifolds admit infinitely many distinct smooth structures.


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Additional Information

Jongil Park
Affiliation: Department of Mathematical Sciences, Seoul National University, San 56-1 Sillim-dong, Gwanak-gu, Seoul 151-747, Korea
Email: jipark@math.snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08818-1
PII: S 0002-9939(07)08818-1
Keywords: Fiber-sum, geography problem, knot surgery, symplectic $4$-manifolds
Received by editor(s): March 23, 2006
Published electronically: March 2, 2007
Additional Notes: This work was supported by Korea Research Foundation Grant (KRF-2004-013-C00002) and R14-2002-007-01002-0
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.