Tree homology and a conjecture of Levine
Tree homology and a conjecture of Levine
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树同调性和莱文猜想
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发表时间：
2010
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影响因子：
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通讯作者：
P. Teichner
中科院分区：
文献类型：
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作者：
James F. Conant;Rob Schneiderman;P. Teichner
J Levine [23] 在对同调圆柱群的研究中，提出了某个群同态 0 W T ! D 0 是同构。 T 和D 0 都是使用三价树组合定义的，并且与各种拓扑设置有很强的联系，包括映射类组、同源柱面、有限类型不变量、惠特尼塔相交理论和Out.Fn/的同源性。在本文中，我们通过将离散莫尔斯理论应用于 Kontsevich 型图复合体的某些子复合体来证实 Levine 的猜想。这些是由树生成的链复合体，我们用莱文图谱的域 T 和范围 D 0 识别它们的特定同源组。同构 0 是对摸索和惠特尼塔索引的链接结构进行分类的关键，如 [6; 中所述。 5]。在本文和[3]中，我们应用我们的结果来证实和改进 Levine 推测的同调圆柱体组的两次过滤之间的关系。 57M27、57M25； 57N10
In his study of the group of homology cylinders, J Levine [23] made the conjecture that a certain group homomorphism 0 W T ! D 0 is an isomorphism. Both T and D 0 are defined combinatorially using trivalent trees and have strong connections to a variety of topological settings, including the mapping class group, homology cylinders, finite type invariants, Whitney tower intersection theory and the homology of Out.Fn/. In this paper, we confirm Levine’s conjecture by applying discrete Morse theory to certain subcomplexes of a Kontsevich-type graph complex. These are chain complexes generated by trees, and we identify particular homology groups of them with the domain T and range D 0 of Levine’s map. The isomorphism 0 is a key to classifying the structure of links up to grope and Whitney tower concordance, as explained in [6; 5]. In this paper and [3] we apply our result to confirm and improve upon Levine’s conjectured relation between two filtrations of the group of homology cylinders. 57M27, 57M25; 57N10
Milnor 不变量和扭曲的惠特尼塔
影响因子：
1.1
作者：
J. Conant;R. Schneiderman;P. Teichner
通讯作者：
P. Teichner