[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7468/jksmeb.2012.19.4.349

GROUPS ACTING ON MEDIAN GRAPHS AND MEDIAN COMPLEXES

Ryang, Dohyoung (The University of North Carolina at Greensboro)

Publication Information

The Pure and Applied Mathematics / v.19, no.4, 2012 , pp. 349-361 More about this Journal

Abstract

CAT(0) cubical complexes are a key to formulate geodesic spaces with nonpositive curvatures. The paper discusses the median structure of CAT90) cubical complexes. Especially, the underlying graph of a CAT(0) cubical complex is a median graph. Using the idea of median structure, this paper shows that groups acting on median complexes L( ${\delta}$ ) groups and, in addition, work L(0) groups are closed under free product.

Keywords

CAT(0) cubical complex; free product; L(0) space; median graph;

Citations & Related Records

Reference

1	M. Bridson & A. Haefliger: Metric Spaces of Non-Positive Curvature. Springer-Verlag, Birlin, 1999.
2	V. Chepoi: Grpahs of some CAT(0) complexes. Advanced Applied Mathematics 24 (2000), 125-179. DOI
3	J. Corson & D. Ryang: Direct product of L-delta groups. Pure and Applied Mathematics 13 (2006), 269-280.
4	J. Corson & D. Ryang: Isoperimetric functions of groups acting on L( $\delta$ ) spaces. Glasgow Math. J. 49 (2007), 1-6. DOI
5	M. Elder: $L_{\delta}$ groups are almost convex and have a sub-cubic dehn function. Algebraic and Geometric Topology 4 (2004), 23-29. DOI
6	M. Gromov: Hyperbolic groups. In S. M. Gersten, editor, Essays in Group Theory, pages 75-263. Springer-Verlag, 1987. Mathematical Science Research Institute Publications 8.
7	M. Neumanann & M. Shapiro: A short course in geometric group theory: Notes for the Australia National University Workshops, 1996
8	G. Niblo & L. Reeves: Groups acting on CAT(0) cube complexes. Geometry and Topology 1 (1997), 1-7. DOI
9	G. Niblo & L. Reeves: The geometry of cube complexes and the complexity of their fundamental groups. Topology 37 (1998), 621-633. DOI
10	G. Niblo & L. Reeves: Coxeter groups acts on CAT(0) cube complexes. J. Group Theory 6 (2003), 399-413.
11	B. Nica: Cubulating spaces with walls. Algebraic and Geometric Topology 4 (2004), 297-309. DOI
12	M. Sageevb: Ends of group pairs ans non-positively curved cube complexes. Proc. London Math. Soc. 71 (1995), 585-671. DOI