Addendum and correction to: “Homology cylinders: an enlargement of the mapping class group”
Addendum and correction to: “Homology cylinders: an enlargement of the mapping class group”
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附录和更正：“同源圆柱：映射类组的扩展”
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Levine
中科院分区：
文献类型：
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作者：
J. Levine
在前一篇文章[同调柱面：映射类群的扩展，代数br.天啊。白杨。1(2001)243-270，Arxiv：Math.gt/0010247]，定义了亏格g的定向曲面上的同调柱面群H_g。利用Goussarov-Habiro的有限型概念，定义了H_g的滤子。错误地认为，这种过滤本质上与相对重量过滤一致。本说明纠正了这一错误，并研究了这两种过滤之间的实际关系。
In a previous paper [Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243--270, arXiv:math.GT/0010247], a group H_g of homology cylinders over the oriented surface of genus g is defined. A filtration of H_g is defined, using the Goussarov-Habiro notion of finite-type. It is erroneously claimed that this filtration essentially coincides with the relative weight filtration. The present note corrects this error and studies the actual relation between the two filtrations.