Acyclic cubical complexes have first been introduced by Bandelt and Chepoi in analogy to acyclic simplicial complexes. They characterized them by cube contraction and elimination schemes and showed that the graphs of acyclic cubical complexes are retracts of cubes characterized by certain forbidden convex subgraphs. In this paper we present an algorithm of time complexity O(m log n) which recog...

We prove a Tits alternative theorem for groups acting on CAT(0) cubical complexes. Namely, suppose that G is a group for which there is a bound on the orders of its finite subgroups. We prove that if G acts properly on a finitedimensional CAT(0) cubical complex, then either G contains a free subgroup of rank 2 or G is finitely generated and virtually abelian. In particular the above conclusion ...

This paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of generalized tori and it is a reflective subcategory of the category of cubical sets. Adjoint functors between the categories of cubical sets and trace monoid actions are constructed. These functors carry independence preserving morphisms in th...

We introduce a new notion of directed homology for cubical sets with connections and transpositions. We show that it respects directed homotopy and is functorial, and that it reduces to the usual homology in case of reversible cubical sets. However it has an undesired cancellation property, which we propose to remedy by refining the dihomology relation.

We study metric conditions implied by a combinatorial curvature condition on a finite cubical 2-complex. Our main result is that any finite, simply connected, cubical 2-complex with the 8-property, admits a strongly convex metric. 2000 Mathematics Subject Classification: 53C21.

The reaction of [PPhJ, NOS,] with CuCl and KSCN (1 :3:3) in acetone produces the yell-ow crystals of [PPh,], [WOS,(CuNCS),]. The crystals are triclinic, space group P1(2), z=2, a=12.4823(7), b=12.9224(7), c=18.6395(10)?, ?=83.907(5), ?= 73.152(4), Y= 65.194(4)'. The crystal structure was determined by single crystal Xray diffraction methods (Mo-K ?) and refined by least-squares calculations ...

the reaction of [pphj, nos,] with cucl and kscn (1 :3:3) in acetone produces the yell-ow crystals of [pph,], [wos,(cuncs),]. the crystals are triclinic, space group p1(2), z=2, a=12.4823(7), b=12.9224(7), c=18.6395(10)?, ?=83.907(5), ?= 73.152(4), y= 65.194(4)'. the crystal structure was determined by single crystal xray diffraction methods (mo-k ?) and refined by least-squares calculation...