Homotopy types of moment-angle complexes for flag complexes
Homotopy types of moment-angle complexes for flag complexes
复制标题
旗形复形的矩角复形的同伦类型
DOI：
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发表时间：
2012
期刊：
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通讯作者：
Jie Wu
中科院分区：
文献类型：
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作者：
J. Grbić;T. Panov;S. Theriault;Jie Wu
我们研究矩角复形的同伦类型，或者等效地，坐标子空间排列的补集的同伦类型。总体目标是识别单纯复形 K，其相应的矩角复形 Z_K 具有球体楔形或球体乘积的连通和的同伦类型。当 K 为 flag 时，我们用代数和组合术语识别那些 Z_K 同伦等价于球体楔子的 K，并给出楔子中球体数量的组合公式。这扩展了伯格伦德和乔伦贝克关于戈洛德环的结果以及第一和第三作者的同伦理论结果。我们还在最小非戈洛德环和矩角复合体 Z_K 之间建立了联系，它们同伦等价于球积的连通和。我们继续证明，对于任何标志复数 K，Z_K 和 DJ(K) 的环空间同伦等价于有理局域化或在任何奇素数处时球体和球体上环的乘积。
We study the homotopy types of moment-angle complexes, or equivalently, of complements of coordinate subspace arrangements. The overall aim is to identify the simplicial complexes K for which the corresponding moment-angle complex Z_K has the homotopy type of a wedge of spheres or a connected sum of sphere products. When K is flag, we identify in algebraic and combinatorial terms those K for which Z_K is homotopy equivalent to a wedge of spheres, and give a combinatorial formula for the number of spheres in the wedge. This extends results of Berglund and Joellenbeck on Golod rings and homotopy theoretical results of the first and third authors. We also establish a connection between minimally non-Golod rings and moment-angle complexes Z_K which are homotopy equivalent to a connected sum of sphere products. We go on to show that for any flag complex K the loop spaces of Z_K and DJ(K) are homotopy equivalent to a product of spheres and loops on spheres when localised rationally or at any odd prime.