论文标题
Artin内核在积极特征中的同源增长
Homological growth of Artin kernels in positive characteristic
论文作者
论文摘要
我们证明了Lück近似定理的类似物，其在某些残留有限的理性可溶性（RFRS）组（包括右角Artin组和BESTVINA组（BESTVINA））中，以阳性特征。具体而言，我们证明，mod $ p $同源性的增长等于组同源性在某个通用分区环中的系数等于尺寸，这与残留链的选择无关。对于一般的RFRS组，我们会在不变性之间获得不平等。我们还考虑了许多应用程序，可用于纤维，可正常的类别和最少的体积熵。
We prove an analogue of the Lück Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin groups and Bestvina--Brady groups. Specifically, we prove that the mod $p$ homology growth equals the dimension of the group homology with coefficients in a certain universal division ring and this is independent of the choice of residual chain. For general RFRS groups we obtain an inequality between the invariants. We also consider a number of applications to fibring, amenable category, and minimal volume entropy.
