论文标题
与多面体产品有关的单层基组和代数
One-relator groups and algebras related to polyhedral products
论文作者
论文摘要
我们通过基础组合链接几何群体理论的不同概念和同义理论。对于旗帜简单的复杂$ k $，我们为右角coxeter组的换向器子组$ rc_k'$ rc_k'指定了一个必要且充分的组合条件，该组被视为真实的Momkle Compleart $ \ Mathcal $ \ Mathcal {R} r} _k $的基本组；对于Pontryagin代数$ H _*（ω\ Mathcal {z} _K）$的矩角综合体是一个单式代数。我们还提供了这些特性的同源表征。对于$ rc_k'$，它是由同源组$ h_2（\ mathcal {r} _k）$的条件给出的，而对于$ h _**（ω\ mathcal {z} _k）$，它以$ \ nathcal {z}}的同源群体的范围表示。
We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$, we specify a necessary and sufficient combinatorial condition for the commutator subgroup $RC_K'$ of a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex $\mathcal{R}_K$, to be a one-relator group; and for the Pontryagin algebra $H_*(Ω\mathcal{Z}_K)$ of the moment-angle complex to be a one-relator algebra. We also give a homological characterisation of these properties. For $RC_K'$, it is given by a condition on the homology group $H_2(\mathcal{R}_K)$, whereas for $H_*(Ω\mathcal{Z}_K)$ it is stated in terms of the bigrading of the homology groups of $\mathcal{Z}_K$.
