Corpus ID: 235731595

Fixed Point Sets in Diagrammatically Reducible Complexes

  title={Fixed Point Sets in Diagrammatically Reducible Complexes},
  author={Shivam Arora and Eduardo Mart'inez-Pedroza},
Let H be a group acting on a simply-connected diagrammatically reducible combinatorial 2-complex X with fine 1skeleton. If the fixed point set X is non-empty, then it is contractible. Having fine 1-skeleton is a weaker version of being locally finite. 1. Diagrammatically reducible complexes The term diagrammatically reducible complex was introduced by Gersten [Ger87], but the notion appeared in earlier works of Chiswell, Collins and Huebschmann [CCH81] and Sieradski [Sie83]. This class of… Expand
1 Citations
Bowditch Taut Spectrum and dimensions of groups
For a finitely generated group G, let H(G) denote Bowditch’s taut loop length spectrum. We prove that if G = (A ∗ B)/〈〈R〉〉 is a C′(1/12) small cancellation quotient of a the free product of finitelyExpand


In Combinatorial group theory and topology (Alta
  • Utah, 1984), volume 111 of Ann. of Math. Stud., pages 53–78. Princeton Univ. Press, Princeton, NJ,
  • 1987
Reducible Diagrams and Equations Over Groups
Diagrammatic reducibility is related to the solution of equations over groups. Sufficient conditions for the reducibility of all spherical diagrams are given, unifying and generalizing work of Adian,Expand
Lifting group actions, equivariant towers and subgroups of non-positively curved groups
If C is a class of complexes closed under taking full subcomplexes and covers and G is the class of groups admitting proper and cocompact actions on one-connected complexes in C , then G is closedExpand
Chiswell , Donald J . Collins , and Johannes Huebschmann . Aspherical group presentations
  • 2012
Relatively hyperbolic Groups
  • B. Bowditch
  • Computer Science, Mathematics
  • Int. J. Algebra Comput.
  • 2012
This paper defines the boundary of a relatively hyperbolic group, and shows that the limit set of any geometrically finite action of the group is equivariantly homeomorphic to this boundary, and generalizes a result of Tukia for geometRically finite kleinian groups. Expand
Fans and Ladders in Small Cancellation Theory
This paper provides a strengthening of the theorems of small cancellation theory. It is proven that disc diagrams contain ‘fans’ of consecutive 2-cells along their boundaries. The size of these fansExpand
  • 87(1-3):161–166,
  • 2001
On Finite Groups Acting on Contractible Complexes of Dimension Two
We show that every action of a finite group on a one-connected diagrammatically reducible two-complex has a fixed point. The proof makes use of Stallings' notion of foldings of graphs, appropriatelyExpand
Diagrammatically reducible complexes and Haken manifolds
  • J. Corson, B. Trace
  • Mathematics
  • Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
  • 2000
Abstract We show that diagrammatically reducible two-complexes are characterized by the property: every finity subconmplex of the universal cover collapses to a one-complex. We use this to show thatExpand
Metric Spaces of Non-Positive Curvature
This book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces byExpand