论文标题
嵌入式接触式束的嵌入式接触同源
Embedded contact homology of prequantization bundles
论文作者
论文摘要
Farris的2011年博士学位论文表明，在riemann表面上的前束束的eCh是同构成其基础同源性外代代数的同构。我们通过计算链复合物上的Z分级来扩展此结果，从而使对这种同构的理解和ECH的稳定性结果更加理解。我们填写了许多技术细节，包括Morse-Bott Direct Limit论点和某些J型塑形建筑物的分类。前者需要在Hutchings-Taubes确立的过滤Seiberg-witter浮子同胞之间的同构和过滤ECH之间的同构。后者要求通过cristofaro-gardiner-hutchings-zhang获得伪层状曲线的较高渐近曲线的工作，以获得对Hutchings-Nelson的相交理论论证的呼吁。
The 2011 PhD thesis of Farris demonstrated that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base. We extend this result by computing the 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. The latter requires the work on higher asymptotics of pseudoholomorphic curves by Cristofaro-Gardiner--Hutchings--Zhang to obtain the writhe bounds necessary to appeal to an intersection theory argument of Hutchings-Nelson.
