Filling invariants of systolic complexes and groups
Filling invariants of systolic complexes and groups
复制标题
收缩期复合波和群的充盈不变量
DOI：
10.2140/gt.2007.11.727
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发表时间：
2007
影响因子：
2
通讯作者：
J. Świa̧tkowski
中科院分区：
文献类型：
--
作者：
T. Januszkiewicz;J. Świa̧tkowski
ATKOWSKI收缩复合体是非正弯曲空间的单纯类似物。他们的理论似乎在很大程度上与CAT（0）立方复形的理论相似。研究了收缩复形中球圈的填充半径，得到了几个推论。我们证明了收缩群不能包含维数严格大于2的非正曲黎曼流形的基本群，尽管存在任意上同调维数的双曲收缩群.我们表明，如果一个收缩组分裂为一个直接的产品，那么这两个因素几乎是免费的。我们还证明了收缩群在2维上满足线性等周不等式。20F69、20F67、20F65
ATKOWSKI Systolic complexes are simplicial analogues of nonpositively curved spaces. Their theory seems to be largely parallel to that of CAT(0) cubical complexes. We study the filling radius of spherical cycles in systolic complexes, and obtain several corollaries. We show that a systolic group can not contain the fundamental group of a nonpositively curved Riemannian manifold of dimension strictly greater than 2, although there exist word hyperbolic systolic groups of arbitrary cohomological dimension. We show that if a systolic group splits as a direct product, then both factors are virtually free. We also show that systolic groups satisfy linear isoperimetric inequality in dimension 2. 20F69, 20F67; 20F65