论文标题
同源性圆柱体和不变的同源性同源性群体与下中央系列有关
Homology cobordism group of homology cylinders and invariants related to lower central series
论文作者
论文摘要
同源性圆柱体的同源性同源性群体是对映射类表面和字符串链接一致性组的概括。我们考虑了约翰逊同构的扩展，该阶级组，Milnor不变性和ORR与同源气缸的链接的不变性，所有这些都与免费的nilpotent群体有关。我们通过扩展的约翰逊同构和扩展的米尔诺不变性的核建立了合并的过滤。我们在三个不变性的情况下确定了它的形象，并研究了不变性之间的关系，以及过滤与自由nilpotent群体的自动形态群体的关系，并分级自由谎言代数。我们通过检查过滤的连续商来获得线性独立不变的数量。
The homology cobordism group of homology cylinders is a generalization of both the mapping class group of surfaces and the string link concordance group. We consider extensions of Johnson homomorphisms of a mapping class group, Milnor invariants and Orr invariants of links to homology cylinders, all of which are related to free nilpotent groups. We establish a combined filtration via kernels of extended Johnson homomorphisms and extended Milnor invariants. We determine its image under the three invariants, and investigate relations among the invariants, and relations of the filtration to automorphism groups of free nilpotent groups and to graded free Lie algebras. We obtain the number of linearly independent invariants by examining the successive quotients of the filtration.
