Bucolic complexes
In this article, we introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. This class of complexes is closed under Cartesian products and amalgamations over some convex subcomplexes. We study various approaches to bucolic complexes: from graph-theoretic and topological viewpoints, as well as from the point of view of geometric group theory. Bucolic complexes can be defined as locally-finite simply connected prism complexes satisfying some local combinatorial conditions. We show that bucolic complexes are contractible, and satisfy some nonpositive-curvature-like properties. In particular, we prove a version of the Cartan-Hadamard theorem, the fixed point theorem for finite group actions, and establish some results on groups acting geometrically on such complexes. We also characterize the 1-skeletons (which we call bucolic graphs) and the 2-skeletons of bucolic complexes. In particular, we prove that bucolic graphs are precisely retracts of Cartesian products of locally finite weakly bridged graphs (i.e., of 1-skeletons of weakly systolic complexes). We show that bucolic graphs are exactly the weakly modular graphs satisfying some local conditions formulated in terms of forbidden induced subgraphs and that finite bucolic graphs can be obtained by gated amalgamations of products of weakly bridged graphs.
2012
2015-07-10 15:28:21
1033
CAT(0) kubni in sistolični kompleksi, medianski in mostovni grafi, zastražena amalgamacija, kartezični produkt, prizmični kompleksi, retrakti, fiksne točke, asferičnost, CAT(0) cubical and systolic complexes, median and bridged graphs, gated amalgamation, Cartesian product, prism complexes, retracts, fixed points, asphericity,
r6
Boštjan
Brešar
70
Jérémie
Chalopin
70
Victor
Chepoi
70
Tanja
Dravec
70
Damian
Osajda
70
UDK
4
519.17:512.5
OceCobissID
13
15706713
COBISS_ID
3
16207961
ISSN pri članku
9
2232-2094
NUK URN
18
URN:SI:UM:DK:WX5QC9R4
0
Predstavitvena datoteka
2015-07-10 15:28:21