arXiv subjects
Publications and source records attributed to Murray J Elder.
In this article we prove that an "isometric multiple HNN-extension" of a group satisfying the falsification by fellow traveler property is almost convex. As a corollary, Wise's example of a CAT(0) non-Hopfian group is Almost convex.
We prove that groups enjoying the falsification by fellow traveler property are of type $F_3$, and have at most an exponential second order isoperimetric function.
We introduce the "loop shortening property" and the "basepoint loop shortening property" for finitely generated groups, and examine their relation to quadratic isoperimetric functions and almost convexity.
We introduce a theory of "patterns" in order to study geodesics in a certain class of group presentations. Using patterns we show that there does not exist a geodesic automatic structure for certain group presentations, and that certain group presentations are almost convex.