Abstract
The main results obtained in Part I can be rephrased in the language of root systems and Euclidean planar tessellations as saying that finite A1 x A1 and A 2 piecewise Euclidean (abbreviated PE) complexes of non-positive curvature have automatic fundamental groups. (A 2-dimensional complex is a A 1 • A1, respectively A2, PE complex if every 2-cell can be identified with a unit square, resp., equilateral triangle in the Euclidean plane, in such a way that the induced metrics agree on intersections. Such a complex has non-positive curvature if the link of each vertex contains no circuits without backtracking of length less than 2 n). Here we prove using similar techniques that finite 2-complexes modelled on the other two root systems, B 2 and G2, corresponding to tessellations by 45 ~ right angle triangles and by 30 ~ 60 ~ right angle triangles, also have automatic fundamental groups (Theorems 2.3 and 3.2). To be precise,
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
