论文标题
旗帜代数和旗帜箱中矩角复合物的LS类别
Pontryagin algebras and the LS-category of moment-angle complexes in the flag case
论文作者
论文摘要
对于任何标志简单的复杂$ k $，我们描述了多面的庞美，关系，关系的最小数量和这些关系的程度，在相应的Moment-Moment-Moment-Moment-Moment-Moment-necor-necorba $ z_k $中的Pontryagin代数中。我们计算$ z_k $的ls类别用于国旗复合体，并在一般情况下给出一个下限。关键的观察结果是，米尔诺 - 摩尔光谱序列在第二张纸上倒塌的旗$ k $。我们还表明，Davis-Januszkiewicz空间的Ponov和Ray的结果对任意系数环有效，并介绍了$（\ Mathbb {Z} \ times \ times \ Mathbb {z}^m）$ - 与pontryagin alggebras of in co y co y co y co y co y co y cone $ zy $ zy $ z。
For any flag simplicial complex $K$, we describe the multigraded Poincare series, the minimal number of relations and the degrees of these relations in the Pontryagin algebra of the corresponding moment-angle complex $Z_K$. We compute the LS-category of $Z_K$ for flag complexes and give a lower bound in the general case. The key observation is that the Milnor-Moore spectral sequence collapses at the second sheet for flag $K$. We also show that the results of Panov and Ray about the Pontryagin algebras of Davis-Januszkiewicz spaces are valid for arbitrary coefficient rings, and introduce the $(\mathbb{Z}\times\mathbb{Z}^m)$-grading on the Pontryagin algebras which is similar to the multigrading on the cohomology of $Z_K$.
