Acylindrical actions on CAT(0) square complexes

Groups Acting on CAT (0) Square Complexes

We study groups acting on CAT (0) square complexes. In particular we show if Y is a nonpositively curved (in the sense of A. D. Alexandrov) finite square complex and the vertex links of Y contain no simple loop consisting of five edges, then any subgroup of π1(Y ) either is virtually free abelian or contains a free group of rank two. In addition we discuss when a group generated by two hyperbol...

Automata and Square Complexes.

We introduce a new geometric tool for analyzing groups of finite au-tomata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reproduc...

Group Actions on Algebraic Cell Complexes

We establish an algebraic version of the classical result that a G-map f between G-complexes which restricts to a homotopy equivalence fH on H-fixed sets for all subgroups H of G is a G-homotopy equivalence. This is used to give an alternative proof of a theorem of Bouc. We also include a number of illustrations and applications.

Circle Actions on Certain 3-cell Complexes

In this paper, we study S actions on a 3-cell complex X having the cohomology of the wedge sum P (n) ∨ S or S ∨ S ∨ S . We determine the possible fixed point sets depending on whether or not X is totally non-homologous to zero in XS1 and give examples of all possible cases.

Partial Actions of Groups on Cell Complexes