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On the Bieri–Neumann–Strebel–Renz invariants of residually free groups
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2020-07-21 , DOI: 10.1017/s0013091520000176 Dessislava H. Kochloukova , Francismar Ferreira Lima
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2020-07-21 , DOI: 10.1017/s0013091520000176 Dessislava H. Kochloukova , Francismar Ferreira Lima
We calculate the Bieri–Neumann–Strebel–Renz invariant Σ1 (G ) for finitely presented residually free groups G and show that its complement in the character sphere S (G ) is a finite union of finite intersections of closed sub-spheres in S (G ). Furthermore, we find some restrictions on the higher-dimensional homological invariants Σn (G , ℤ) and show for the discrete points Σ2 (G )dis , Σ2 (G , ℤ)dis and Σ2 (G , ℚ)dis in Σ2 (G ), Σ2 (G , ℤ) and Σ2 (G , ℚ) that we have the equality Σ2 (G )dis = Σ2 (G , ℤ)dis = Σ2 (G , ℚ)dis .
中文翻译:
关于剩余自由群的 Bieri-Neumann-Strebel-Renz 不变量
我们计算 Bieri–Neumann–Strebel–Renz 不变量 Σ1 (G ) 对于有限呈现的剩余自由群G 并表明它在字符范围内的补码小号 (G ) 是封闭子球体的有限交集的有限并集小号 (G )。此外,我们发现对高维同调不变量 Σ 的一些限制n (G , ℤ) 并显示离散点 Σ2 (G )迪斯 , Σ2 (G , ℤ)迪斯 和 Σ2 (G , ℚ)迪斯 在 Σ2 (G ), Σ2 (G , ℤ) 和 Σ2 (G , ℚ) 我们有等式 Σ2 (G )迪斯 = Σ2 (G , ℤ)迪斯 = Σ2 (G , ℚ)迪斯 .
更新日期:2020-07-21
中文翻译:
关于剩余自由群的 Bieri-Neumann-Strebel-Renz 不变量
我们计算 Bieri–Neumann–Strebel–Renz 不变量 Σ