Characterization of Y2-Equivalence for Homology Cylinders
Characterization of Y2-Equivalence for Homology Cylinders
复制标题
同调圆柱体 Y2 等价的表征
DOI：
10.1142/s0218216503002585
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发表时间：
2002
影响因子：
0.5
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
G. Massuyeau;Jean
对于一个紧连通的定向曲面，我们考虑了上的同调柱面：这些是具有额外同调平凡条件的同调协边。当考虑到Y2-等价时，这是一个由Goussarov-Habiro理论产生的手术等价关系，同调圆柱形成阿贝尔群。当图群有一个或零个边界分支时，本文定义了从一个图空间到这个图空间的外科手术映射。证明了该映射是一个同构，其逆映射由第一约翰逊同态和Birman-Craggs同态的某些扩张给出。
For Σ a compact connected oriented surface, we consider homology cylinders over Σ: these are homology cobordisms with an extra homological triviality condition. When considered up to Y2-equivalence, which is a surgery equivalence relation arising from the Goussarov-Habiro theory, homology cylinders form an Abelian group. In this paper, when Σ has one or zero boundary component, we define a surgery map from a certain space of graphs to this group. This map is shown to be an isomorphism, with inverse given by some extensions of the first Johnson homomorphism and Birman-Craggs homomorphisms.