A uniform model for almost convexity and rewriting systems
نویسندگان
چکیده
منابع مشابه
A Uniform Model for Almost Convexity and Rewriting Systems
We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define algorithmically stackable groups, for which this procedure is an algorithm. This property gives a common model for algorithms arising from both rewriting syste...
متن کاملTame combings, almost convexity and rewriting systems for groups
A finite complete rewriting system for a group is a finite presentation which gives an algorithmic solution to the word problem. Finite complete rewriting systems have proven to be useful objects in geometric group theory, yet little is known about the geometry of groups admitting such rewriting systems. We show that a group G with a finite complete rewriting system admits a tame 1-combing; it ...
متن کاملMinimal Almost Convexity
In this article we show that the Baumslag-Solitar group BS(1, 2) is minimally almost convex, or MAC. We also show that BS(1, 2) does not satisfy Poénaru’s almost convexity condition P (2), and hence the condition P (2) is strictly stronger than MAC. Finally, we show that the groups BS(1, q) for q ≥ 7 and Stallings’ non-FP3 group do not satisfy MAC. As a consequence, the condition MAC is not a c...
متن کاملThe Loop Shortening Property and Almost Convexity
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.
متن کاملTame Combing and Almost Convexity Conditions
We explore relationships between the family of successively weaker almost convexity conditions, and successively weaker tame combing conditions. We show that both Thompson’s group F and the Baumslag-Solitar groups BS(1, p) with p ≥ 3 admit a tame combing with a linear radial tameness function. By earlier work of Belk and Bux showing that F is not minimally almost convex, and of Elder and Hermil...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2015
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgth-2015-0011