arXiv math/06076082006-07math.GT

Rational blow-down along Wahl type plumbing trees of spheres

Maria Michalogiorgaki

备注：: 17 pages, 8 figures, v2: structural revision, accepted for publication in Algebraic & Geometric Topology
发表信息：: Algebr. Geom. Topol. 7 (2007) 1327-1343
DOI：: 10.2140/agt.2007.7.1327

英文摘要：

We construct smooth 4-manifolds homeomorphic but not diffeomorphic to $CP^2#k\bar{CP^2},k \in {6,7,8,9}$, using the technique of rational blow-down along Wahl type plumbing trees of spheres.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Symplectically replacing plumbings with Euler characteristic 2 4-manifolds

We introduce new symplectic cut-and-paste operations that generalize the rational blowdown. In particular, we will define $k$-replaceable plumbings to be those that, heuristically, can be symplectically replaced by Euler characteristic $k$ 4-manifolds. We will then classify 2-replaceable linear plumbings, construct 2-replaceable plumbing trees, and use one such tree to construct a symplectic exotic $\mathbb{C}P^2\#6\overline{\mathbb{C}P^2}$.

2020-11-05math.GT

A note on symplectic rational blow--downs

Due to a significant error in the main result (pointed out by J. Wahl), the paper has been withdrawn by the authors. A corrected and expanded version is 'Rational blow-downs and smoothings of surface singularities' by A. Stipsicz, Z. Szabo and J. Wahl.

2006-11-06math.GTmath.SG

Surgery along star shaped plumbings and exotic smooth structures on 4-manifolds

We define a new 4-dimensional symplectic cut and paste operation which is analogous to Fintushel and Stern's rational blow-down. We use this operation to produce multiple constructions of symplectic smoothly exotic complex projective space blown-up eight times, seven times, and six times. We also show how this operation can be used in conjunction with knot surgery to construct an infinite family of minimal exotic smooth structures on the complex projective space blown-up seven times.

2015-09-12math.GTmath.SG

Symplectic rational blow-down along Seifert fibered 3-manifolds

We verify that the rational blow-down schemes along certain Seifert fibered 3-manifolds found by the second author, Szabo and Wahl are, in fact, symplectic operations.

2007-07-26math.GTmath.SG

Rational blow-downs and smoothings of surface singularities

In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing. New examples of surface singularities with rational homology disk smoothings are also presented; these include singularities with resolution graph having valency four nodes.

2008-03-13math.AGmath.GT

Small exotic 4-manifolds from lines and quadrics in $\mathbb{CP}^{2}$

We construct potentially new manifolds homeomorphic but not diffeomorphic to $\mathbb{CP}^{2} \# 8 \overline{\mathbb{CP}^{2}}$ and $\mathbb{CP}^{2} \# 9 \overline{\mathbb{CP}^{2}}$ via rational blowdown surgery along certain $4$-valent plumbing graphs. This way all the graph classes from \cite{weighted} have a representative which admits a rational blowdown leading to an exotic manifold. We emphasize the simplicity of the constructions which boils down to finding a good configuration of complex lines and quadrics in $\mathbb{CP}^{2}$, and deciding which intersections to blow up.

2019-04-29math.GT

更多相关论文收起更多论文

The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof

Splice type surface singularities, introduced in 2002 by Neumann and Wahl, provide all examples known so far of integral homology spheres which appear as links of complex isolated complete intersections of dimension two. They are determined, up to a form of equisingularity, by decorated trees called splice diagrams. In 2005, Neumann and Wahl formulated their Milnor fiber conjecture, stating that any choice of an internal edge of a splice diagram determines a special kind of decomposition into pieces of the Milnor fibers of the associated singularities. These pieces are constructed from the Mil…

2022-12-06math.AGmath.GT

Symplectic Rational Blow-up

Fintushel and Stern defined the rational blow-down construction [FS] for smooth 4-manifolds, where a linear plumbing configuration of spheres $C_n$ is replaced with a rational homology ball $B_n$, $n \geq 2$. Subsequently, Symington [Sy] defined this procedure in the symplectic category, where a symplectic $C_n$ (given by symplectic spheres) is replaced by a symplectic copy of $B_n$ to yield a new symplectic manifold. As a result, a symplectic rational blow-down can be performed on a manifold whenever such a configuration of symplectic spheres can be found. In this paper, we define the inverse…

2013-03-11math.GTmath.SG

Symplectic fillings of Seifert fibered spaces

We give finiteness results and some classifications up to diffeomorphism of minimal strong symplectic fillings of Seifert fibered spaces over S^2 satisfying certain conditions, with a fixed natural contact structure. In some cases we can prove that all symplectic fillings are obtained by rational blow-downs of a plumbing of spheres. In other cases, we produce new manifolds with convex symplectic boundary, thus yielding new cut-and-paste operations on symplectic manifolds containing certain configurations of symplectic spheres.

2013-09-25math.GTmath.SG

Symplectic 4-Manifolds on the Noether Line and between the Noether and Half Noether Lines

We construct simply connected, minimal, symplectic 4-manifolds with exotic smooth structures and each with one Seiberg-Witten basic class up to sign, on the Noether line and between the Noether and half Noether lines by star surgeries introduced by Karakurt and Starkston, and by using complex singularities. We also construct certain configurations of complex singularities in the rational elliptic surfaces geometrically, without using any monodromy arguments. By using these configurations, we give symplectic embeddings of star shaped plumbings inside (some blow-ups of) elliptic surfaces.

2021-09-15math.AGmath.GTmath.SG