Embedded contact homology of prequantization bundles

IF 0.6 3区 数学 Q3 MATHEMATICS
Jo Nelson, Morgan Weiler
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引用次数: 0

Abstract

The 2011 PhD thesis of Farris [Fa] demonstrated that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a $\mathbb{Z}^2$-graded group to the exterior algebra of the homology of its base. We extend this result by computing the $\ mathbb{Z}$-grading on the chain complex, permitting a finer understanding of this isomorphism and a stability result for ECH. We fill in a number of technical details, including the Morse–Bott direct limit argument and the classification of certain $J$-holomorphic buildings. The former requires the isomorphism between filtered Seiberg–Witten Floer cohomology and filtered ECH as established by Hutchings–Taubes [HT13]. The latter requires the work on higher asymptotics of pseudoholomorphic curves by Cristofaro-Gardiner–Hutchings–Zhang [CGHZ] to obtain the writhe bounds necessary to appeal to an intersection theory argument of Hutchings–Nelson [HN16].
预量化束的嵌入接触同源性
2011 年法里斯的博士论文[Fa]证明了黎曼曲面上预量化束的 ECH 作为 $\mathbb{Z}^2$ 阶群与其基底同调的外部代数是同构的。我们通过计算链复数上的($\mathbb{Z}^2$)分级来扩展这一结果,从而可以更精细地理解这一同构性,并得出 ECH 的稳定性结果。我们补充了一些技术细节,包括莫尔斯-波特直接极限论证和某些$J$同构建筑的分类。前者需要哈钦斯-陶布斯(Hutchings-Taubes)[HT13]建立的过滤塞伯格-维滕弗洛尔同调与过滤 ECH 之间的同构。后者需要克里斯托法罗-加迪纳-哈钦斯-张[CGHZ]关于伪全形曲线的高渐近性的工作,以获得必要的writhe边界,从而诉诸哈钦斯-纳尔逊[HN16]的交集理论论证。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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