scholarly journals Minimal almost convexity

2005 ◽  
Vol 8 (2) ◽  
Author(s):  
Murray Elder ◽  
Susan Hermiller
Keyword(s):  
Almost Convexity

scholarly journals The Loop Shortening Property and Almost Convexity

2003 ◽  
Vol 102 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Murray J. Elder
Keyword(s):  
Almost Convexity

scholarly journals Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles

2017 ◽  
Vol 2019 (13) ◽  
pp. 4004-4046
Author(s):  
Corey Bregman
Keyword(s):  
Unit Circle ◽  
Dimensional Torus ◽  
Torus Bundle ◽  
Generating Set ◽  
Growth Series ◽  
Torus Bundles ◽  
Almost Convex ◽  
Higher Dimensional ◽  
Finite Index Subgroup ◽  
Almost Convexity

AbstractGiven a matrix $A\in SL(N,\mathbb{Z})$, form the semidirect product $G=\mathbb{Z}^N\rtimes_A \mathbb{Z}$ where the $\mathbb{Z}$-factor acts on $\mathbb{Z}^N$ by $A$. Such a $G$ arises naturally as the fundamental group of an $N$-dimensional torus bundle which fibers over the circle. In this article, we prove that if $A$ has distinct eigenvalues not lying on the unit circle, then there exists a finite index subgroup $H\leq G$ possessing rational growth series for some generating set. In contrast, we show that if $A$ has at least one eigenvalue not lying on the unit circle, then $G$ is not almost convex for any generating set.

A certain condition of almost convexity

1983 ◽  
Vol 35 (2) ◽  
pp. 146-149 ◽  
Author(s):  
V. V. Ostapenko
Keyword(s):  
Almost Convexity

scholarly journals Tame combings, almost convexity and rewriting systems for groups

1997 ◽  
Vol 225 (2) ◽  
pp. 263-276 ◽  
Author(s):  
Susan M. Hermiller ◽  
John Meier
Keyword(s):  
Rewriting Systems ◽  
Almost Convexity

scholarly journals Tame combing and almost convexity conditions

2010 ◽  
Vol 269 (3-4) ◽  
pp. 879-915 ◽  
Author(s):  
Sean Cleary ◽  
Susan Hermiller ◽  
Melanie Stein ◽  
Jennifer Taback
Keyword(s):  
Almost Convexity ◽  
Convexity Conditions

scholarly journals Almost convexity and quantitative korovkin type results

1998 ◽  
Vol 11 (4) ◽  
pp. 105-108 ◽  
Author(s):  
F.J. Muñoz-Delgado ◽  
D. Cárdenas-Morales
Keyword(s):  
Almost Convexity
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