Knotted surfaces in 4-manifolds
Knotted surfaces in 4-manifolds
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4 流形中的结曲面
DOI：
10.1515/form.2011.130
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发表时间：
2008
影响因子：
0.7
通讯作者：
Thomas E. Mark
中科院分区：
文献类型：
--
作者：
Thomas E. Mark
抽象的。Fintushel和Stern证明了：如果是辛4-流形中的辛曲面，使得有单连通补和非负自交，则存在无穷多个拓扑等价但光滑不同的嵌入曲面。在这里，我们将这一结果推广到包括辛曲面，其自相交是有界的，其中g是亏格。我们使用的工具，从Heegaard Floer理论，并包括几个结果，可能是独立的利益。具体来说，我们给出了一个类似的Ozsváth-Szabó不变量的Fintushel-Stern结手术公式的Seiberg-Witten不变量，无论是封闭的4-流形和流形的边界。这是基于一个公式的Ozsváth-Szabó不变量的结果的对数变换，类似于一个获得的摩根-Mrowka-Szabó的塞伯格-威滕不变量，和结果的Ozsváth-Szabó不变量的纤维总和由于作者和Jabuka。此外，我们还计算了黎曼曲面上“大”度圆丛的扭曲Heegaard Floer同调。
Abstract. Fintushel and Stern have proved that if is a symplectic surface in a symplectic 4-manifold such that has simply-connected complement and nonnegative self-intersection, then there are infinitely many topologically equivalent but smoothly distinct embedded surfaces homologous to . Here we extend this result to include symplectic surfaces whose self-intersection is bounded below by , where g is the genus of . We make use of tools from Heegaard Floer theory, and include several results that may be of independent interest. Specifically we give an analogue for Ozsváth–Szabó invariants of the Fintushel–Stern knot surgery formula for Seiberg–Witten invariants, both for closed 4-manifolds and manifolds with boundary. This is based on a formula for the Ozsváth–Szabó invariants of the result of a logarithmic transformation, analogous to one obtained by Morgan–Mrowka–Szabó for Seiberg–Witten invariants, and the results on Ozsváth–Szabó invariants of fiber sums due to the author and Jabuka. In addition, we give a calculation of the twisted Heegaard Floer homology of circle bundles of “large” degree over Riemann surfaces.