摘要翻译:
本文计算了本原链群的pro-p完备的Galois上同调。这里,本原链环群是3-球面上一个驯服链环的基本群,它的链环数图是不可约的模p(例如,没有一个链环数是可被p整除的)。结果表明(在Z/PZ-系数下)Galois上同调与离散链群的Z/PZ-上同调是天然同构的。这个结果的主要应用是,对于这样的群,Baum-Connes猜想或Atiyah猜想对于每一个有限扩张(甚至每一个初等允许扩张)都是真的,如果它们对于群本身是真的的话。
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英文标题:
《Galois cohomology of completed link groups》
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作者:
Inga Blomer (Georg-August-Universitaet Goettingen), Peter Linnell
(Virginia Tech), Thomas Schick (Georg-August-Universitaet Goettingen)
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Group Theory 群论
分类描述:Finite groups, topological groups, representation theory, cohomology, classification and structure
有限群、拓扑群、表示论、上同调、分类与结构
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
In this paper we compute the Galois cohomology of the pro-p completion of primitive link groups. Here, a primitive link group is the fundamental group of a tame link in the 3-sphere whose linking number diagram is irreducible modulo p (e.g. none of the linking numbers is divisible by p). The result is that (with Z/pZ-coefficients) the Galois cohomology is naturally isomorphic to the Z/pZ-cohomology of the discrete link group. The main application of this result is that for such groups the Baum-Connes conjecture or the Atiyah conjecture are true for every finite extension (or even every elementary amenable extension), if they are true for the group itself.
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PDF链接:
https://arxiv.org/pdf/0708.3727