从三分图计算四流形的同调与交形。
Calculating the homology and intersection form of a 4-manifold from a trisection diagram.
机构信息
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland.
Department of Mathematics, University of California, Berkeley, CA 94720.
出版信息
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10869-10874. doi: 10.1073/pnas.1717176115.
Given a diagram for a trisection of a 4-manifold X, we describe the homology and the intersection form of X in terms of the three subgroups of [Formula: see text] generated by the three sets of curves and the intersection pairing on [Formula: see text] This includes explicit formulas for the second and third homology groups of X as well an algorithm to compute the intersection form. Moreover, we show that all [Formula: see text]-trisections admit "algebraically trivial" diagrams.
给定一个 4 维流形 X 的三分图，我们用由三组曲线生成的 [Formula: see text] 的三个子群以及 [Formula: see text] 上的交配对 X 的同调群和交积形式进行描述。这包括 X 的第二和第三同调群的显式公式以及计算交积形式的算法。此外，我们证明所有 [Formula: see text]-三分图都允许“代数平凡”的图。
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