[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b200389

ALGEBRAIC RANKS OF THE FUNDAMENTAL GROUPS OF HIGH DIMENSIONAL GRAPH MANIFOLDS

Kim, Raeyong (Department of Mathematics Daegu University)

Publication Information

Bulletin of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 527-535 More about this Journal

Abstract

The fundamental group of a high dimensional graph manifold canonically has a graph of groups structure. We analyze the group action on the associated Bass-Serre tree and study the algebraic ranks of the fundamental groups of high dimensional graph manifolds.

Keywords

Algebraic rank of a group; high dimensional graph manifolds; graph of groups; Bass-Serre theory;

Citations & Related Records

Reference

1	W. Ballmann, Nonpositively curved manifolds of higher rank, Ann. of Math. (2) 122 (1985), no. 3, 597-609. https://doi.org/10.2307/1971331 DOI
2	W. Ballmann and P. Eberlein, Fundamental groups of manifolds of nonpositive curvature, J. Differential Geom. 25 (1987), no. 1, 1-22. http://projecteuclid.org/euclid.jdg/1214440722
3	B. H. Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012), no. 3, 1250016, 66 pp. https://doi.org/10.1142/S0218196712500166 DOI
4	K. Burns and R. Spatzier, Manifolds of nonpositive curvature and their buildings, Inst. Hautes Etudes Sci. Publ. Math. No. 65 (1987), 35-59. DOI
5	T. Delzant, Sur l'accessibilite acylindrique des groupes de presentation finie, Ann. Inst. Fourier (Grenoble) 49 (1999), no. 4, 1215-1224. DOI
6	R. Frigerio, J.-F. Lafont, and A. Sisto, Rigidity of high dimensional graph manifolds, Asterisque No. 372 (2015), xxi+177 pp.
7	A. Ould Houcine, Embeddings in finitely presented groups which preserve the center, J. Algebra 307 (2007), no. 1, 1-23. https://doi.org/10.1016/j.jalgebra.2006.07.015 DOI
8	P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419-436. https://doi.org/10.1112/plms/s3-4.1.419 DOI
9	R. Kim, Algebraic ranks of CAT(0) groups, Algebraic & Geometric Topology 14 (2014), no. 3, 1627-1648. DOI
10	D. V. Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc. 179 (2006), no. 843, vi+100 pp. https://doi.org/10.1090/memo/0843 DOI
11	G. Prasad and M. S. Raghunathan, Cartan subgroups and lattices in semi-simple groups, Ann. of Math. (2) 96 (1972), 296-317. https://doi.org/10.2307/1970790 DOI
12	J.-P. Serre, Trees, translated from the French by John Stillwell, Springer-Verlag, Berlin, 1980.