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Algebraic ranks of the fundamental groups of high dimensional graph manifolds

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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.

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.

참고문헌 (12)

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  5. T. Delzant, "Sur l’accessibilit´e acylindrique des groupes de pr´esentation finie", Ann. Inst. Fourier(Grenoble), 49(4), pp.1215~1224 (1999)
  6. R. Frigerio, "Rigidity of high dimensional graph manifolds", Ast´erisque, (372), pp.xxi+177~ (2015)
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  8. R. Kim, "Algebraic ranks of CAT(0) groups", Algebraic & Geometric Topology, 14(3), pp.1627~1648 (2014)
  9. D. V. Osin, "Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems", Mem. Amer. Math. Soc, 179(843), pp.vi+100~ (2006)[DOI]
  10. Abderezak Ould Houcine, "Embeddings in finitely presented groups which preserve the center", Journal of Algebra, 307(1), pp.1~23 (2007), Elsevier BV[DOI]
  11. G. Prasad, "Cartan subgroups and lattices in semi-simple groups", Ann. of Math, 96(2), pp.296~317 (1972)[DOI]
  12. J. -P. Serre, "Trees, translated from the French by John Stillwell" (1980), Springer-Verlag

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