论文标题
mod $ p $和非阳性曲率的扭力同源性增长
Mod $p$ and torsion homology growth in nonpositive curvature
论文作者
论文摘要
我们计算有限指数的剩余序列的Mod $ p $同源性增长正常的右角Artin组。我们发现这与理性同源性增长不同的例子，这意味着序列中亚组的同源性具有很大的扭曲。更确切地说，同源性扭转在亚组的索引中呈指数增长。对于Odd Primes $ P $，我们构建了封闭的本地CAT（0）歧管，而非零mod $ p $同源性增长在中间维度之外。这些例子表明，歌手对理性同源性增长的猜想，而吕克（Lück）对扭转同源性生长的猜想彼此不相容，因此至少其中一个必须是错误的。
We compute the mod $p$ homology growth of residual sequences of finite index normal subgroups of right-angled Artin groups. We find examples where this differs from the rational homology growth, which implies the homology of subgroups in the sequence has lots of torsion. More precisely, the homology torsion grows exponentially in the index of the subgroup. For odd primes $p$, we construct closed locally CAT(0) manifolds with nonzero mod $p$ homology growth outside the middle dimension. These examples show that Singer's conjecture on rational homology growth and Lück's conjecture on torsion homology growth are incompatible with each other, so at least one of them must be wrong.
