论文标题
三个manifold小组的有限商
Finite quotients of 3-manifold groups
论文作者
论文摘要
对于$ g $和$ h_1，\ dots，h_n $有限组，是否存在$ 3 $ - manifold group，$ g $作为商，但没有$ h_i $作为商？我们根据有限群体的群体共同体来回答所有此类问题。我们证明不存在拓扑结果，从而推广了半分类理论。为了证明存在具有某些有限的商但没有其他有限的3个模型，我们首先使用概率方法，首先证明了在Dunfield-Thurston模型中的随机3个manifold的基本组的分布的公式，该组是随机的heegaard划分模型，因为该模型是Infinity属。我们认为，这是从其时刻开始对随机组进行新的分布的第一个结构。
For $G$ and $H_1,\dots, H_n$ finite groups, does there exist a $3$-manifold group with $G$ as a quotient but no $H_i$ as a quotient? We answer all such questions in terms of the group cohomology of finite groups. We prove non-existence with topological results generalizing the theory of semicharacteristics. To prove existence of 3-manifolds with certain finite quotients but not others, we use a probabilistic method, by first proving a formula for the distribution of the (profinite completion of) the fundamental group of a random 3-manifold in the Dunfield-Thurston model of random Heegaard splittings as the genus goes to infinity. We believe this is the first construction of a new distribution of random groups from its moments.
