Smooth structures on complex surfaces with fundamental group $\mathbf {Z}_2$

Wang, Shuguang

doi:10.1090/s0002-9939-97-03641-1

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…An immediate consequence of Theorem 17 is the study of the geography and botany of irreducible symplectic 4-manifolds for various fundamental groups (cf. [38,36,42,29,30,31,74,27,10,43,57,12,13,4,2,6,71,76]). In particular, the following result extends [71, Theorem 1].…”

Section: Theorem 17 Existence Of Telescoping Triplesmentioning

confidence: 99%

“…We build greatly upon the recent constructions to systematically study the geography and botany of irreducible symplectic 4-manifolds with abelian fundamental groups. The first examples of exotic 4-manifolds with cyclic fundamental group were constructed in [36,38,29,42,30,74,18,27,13,4], and examples of 4-manifolds with finite fundamental group can be found in [30,27]. Examples of minimal symplectic 4-manifolds with fundamental group Z ⊕ Z p had been previously built in [27,43,57].…”

Section: Introductionmentioning

confidence: 99%

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Geography and Botany of Irreducible Non-Spin Symplectic 4-Manifolds With Abelian Fundamental Group

Torres

2013

Glasgow Math. J.

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Abstract. The geography and botany problems of irreducible non-spin symplectic 4-rnanifolds with a choice of fundamental group from {lp . "llp EB "ll.q, l, Z EB Zp, ZEB Z} are studied by building upon the recent progress obtained on the simply con nected realm. R esults on the botany of simply connected 4-manifolds not available in the literature are extended .2010 Mathematics Subject Classification. Primary 57R 17; Secondary 57M05, 54D051. Introduction. Topologists' understanding of smooth 4-manifolds has witnessed a drastic improvement during the last 20 years. Advances in symplectic geometry [8,25,31,35,[65][66][67]71] and inventions of gluing formulas [39,46] for diff eomorphism invariants (73] have paired elegantly with topological constructions [16,18,[19][20][21], offering a noteworthy insight into the smooth four-dimensional story. The most recent series of successes [2-4, 6, 11, 16, 21 ] has answered as many questions as it has raised new ones, and the 4-manifolds theory remains to be an intriguing and active area of research.Two factors responsible for the recent progress on the simply connected realm are the increase in the repertoire of techniques that manufacture symplectic 4-manifolds with sm all topological invariants, and a new perspective on the usage of already existing mechanisms of construction. The idea of using symplectic sums (25) of non-simply connected building blocks along genus 2 surfaces to kill fundamenta l groups in an efficient way was introduced in (1). Its immediate outcome was the

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Section: Theorem 17 Existence Of Telescoping Triplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geography and Botany of Irreducible Non-Spin Symplectic 4-Manifolds With Abelian Fundamental Group

Torres

2013

Glasgow Math. J.

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Anti-holomorphic involutions and almost complex structures on four-manifold

Gao

1989

Sci. China Ser. A-Math.

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Finite group actions on 4-manifolds

Cho

1999

J Aust Math Soc A

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Let X be a closed, oriented, smooth 4-manifold with a finite fundamental group and with a non-vanishing Seiberg-Witten invariant. Let G be a finite group. If G acts smoothly and freely on X, then the quotient X/G cannot be decomposed as X^X-i with £^(X,) > 0, i = 1, 2. In addition let X be symplectic and C|(X) 2 > 0 and b^(X) > 3. If a is a free anti-symplectic involution on X then the Seiberg-Witten invariants on X/a vanish for all spin c structures on X/a, and if IJ is a free symplectic involution on X then the quotients X/a and X/rj are not diffeomorphic to each other.1991 Mathematics subject classification (Amen Math. Soc): primary 57R55,57N13, 57S17.

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Smooth structures on complex surfaces with fundamental group $\mathbf {Z}_2$

Abstract: Abstract. It is shown that the quotients of a complex surface under free holomorphic and anti-holomorphic involutions are homeomorphic but not diffeomorphic. This gives a way to construct exotic smooth structures on some complex surfaces.

Cited by 4 publications

References 19 publications

Geography and Botany of Irreducible Non-Spin Symplectic 4-Manifolds With Abelian Fundamental Group

Geography and Botany of Irreducible Non-Spin Symplectic 4-Manifolds With Abelian Fundamental Group

Anti-holomorphic involutions and almost complex structures on four-manifold

Finite group actions on 4-manifolds

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