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Coarse flow spaces for relatively hyperbolic groups

  • A. Bartels (a1)


We introduce coarse flow spaces for relatively hyperbolic groups and use them to verify a regularity condition for the action of relatively hyperbolic groups on their boundaries. As an application the Farrell–Jones conjecture for relatively hyperbolic groups can be reduced to the peripheral subgroups (up to index-2 overgroups in the $L$ -theory case).



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[ACG15] Antolín, Y., Coulon, R. and Gandini, G., Farrell–Jones via Dehn fillings, Preprint (2015),arXiv:1510.08113v1.
[BFL14] Bartels, A., Farrell, F. T. and Lück, W., The Farrell–Jones conjecture for cocompact lattices in virtually connected Lie groups , J. Amer. Math. Soc. 27 (2014), 339388.
[BL12a] Bartels, A. and Lück, W., The Borel conjecture for hyperbolic and CAT(0)-groups , Ann. of Math. (2) 175 (2012), 631689.
[BL12b] Bartels, A. and Lück, W., Geodesic flow for CAT(0)-groups , Geom. Topol. 16 (2012), 13451391.
[BLR08a] Bartels, A., Lück, W. and Reich, H., Equivariant covers for hyperbolic groups , Geom. Topol. 12 (2008), 17991882.
[BLR08b] Bartels, A., Lück, W. and Reich, H., The K-theoretic Farrell–Jones conjecture for hyperbolic groups , Invent. Math. 172 (2008), 2970.
[BLR08c] Bartels, A., Lück, W. and Reich, H., On the Farrell–Jones conjecture and its applications , J. Topol. 1 (2008), 5786.
[BLRR14] Bartels, A., Lück, W., Reich, H. and Rüping, H., K- and L-theory of group rings over GL n (Z) , Publ. Math. Inst. Hautes Études Sci. 119 (2014), 97125.
[BR07] Bartels, A. and Reich, H., Coefficients for the Farrell–Jones conjecture , Adv. Math. 209 (2007), 337362.
[Bas72] Bass, H., The degree of polynomial growth of finitely generated nilpotent groups , Proc. Lond. Math. Soc. (3) 25 (1972), 603614.
[BM91] Bestvina, M. and Mess, G., The boundary of negatively curved groups , J. Amer. Math. Soc. 4 (1991), 469481.
[Bor67] Borsuk, K., Theory of retracts, Monografie Matematyczne, vol. 44 (Państwowe Wydawnictwo Naukowe, Warsaw, 1967).
[Bow12] Bowditch, B. H., Relatively hyperbolic groups , Internat. J. Algebra Comput. 22 (2012), 1250016, 66.
[BH99] Bridson, M. R. and Haefliger, A., Metric spaces of non-positive curvature, Die Grundlehren der mathematischen Wissenschaften, vol. 319 (Springer, Berlin, 1999).
[Dah03] Dahmani, F., Classifying spaces and boundaries for relatively hyperbolic groups , Proc. Lond. Math. Soc. (3) 86 (2003), 666684.
[DQR11] Davis, J. F., Quinn, F. and Reich, H., Algebraic K-theory over the infinite dihedral group: a controlled topology approach , J. Topol. 4 (2011), 505528.
[Els08] Elsner, T., Systolic groups with isolated flats, Preprint (2008).
[Far98] Farb, B., Relatively hyperbolic groups , Geom. Funct. Anal. 8 (1998), 810840.
[FJ86] Farrell, F. T. and Jones, L. E., K-theory and dynamics. I , Ann. of Math. (2) 124 (1986), 531569.
[FJ93] Farrell, F. T. and Jones, L. E., Isomorphism conjectures in algebraic K-theory , J. Amer. Math. Soc. 6 (1993), 249297.
[FR00] Farrell, F. T. and Roushon, S. K., The Whitehead groups of braid groups vanish , Int. Math. Res. Not. IMRN 10 (2000), 515526.
[Gro87] Gromov, M., Hyperbolic groups , in Essays in group theory (Springer, New York, 1987), 75263.
[Gro93] Gromov, M., Asymptotic invariants of infinite groups , in Geometric group theory, Vol. 2 (Sussex, 1991) (Cambridge University Press, Cambridge, 1993), 1295.
[GM08] Groves, D. and Manning, J. F., Dehn filling in relatively hyperbolic groups , Israel J. Math. 168 (2008), 317429.
[HW41] Hurewicz, W. and Wallman, H., Dimension theory, Princeton Mathematical Series, vol. 4. (Princeton University Press, Princeton, NJ, 1941).
[KR15] Kasprowski, D. and Rüping, H., Long and thin covers for cocompact flow spaces, Preprint (2015), arXiv:1502.05001.
[Lue10] Lück, W., K- and L-theory of group rings , in Proceedings of the international congress of mathematicizans, Vol. II (Hindustan Book Agency, New Delhi, 2010), 10711098.
[LR05] Lück, W. and Reich, H., The Baum–Connes and the Farrell–Jones conjectures in K- andL-theory , in Handbook of K-theory, Vols. 1, 2 (Springer, Berlin, 2005), 703842.
[Min05] Mineyev, I., Flows and joins of metric spaces , Geom. Topol. 9 (2005), 403482 (electronic).
[MY] Mineyev, I. and Yaman, A., Relative hyperbolicity and bounded cohomology, Preprint,∼mineyev/math/art/rel-hyp.pdf.
[Mol13] Mole, A., Extending a metric on a simplicial complex, Preprint (2013), arXiv:1309.0981.
[MR13] Mole, A. and Rüping, H., Equivariant refinements, Preprint (2013), arXiv:1308.2799.
[Osi05] Osin, D., Asymptotic dimension of relatively hyperbolic groups , Int. Math. Res. Not. IMRN 35 (2005), 21432161.
[Oza06a] Ozawa, N., Amenable actions and applications , in International congress of mathematicians, Vol. II (European Mathematical Society, Zürich, 2006), 15631580.
[Oza06b] Ozawa, N., Boundary amenability of relatively hyperbolic groups , Topology Appl. 153 (2006), 26242630.
[Pea75] Pears, A. R., Dimension theory of general spaces (Cambridge University Press, Cambridge, 1975).
[Qui12] Quinn, F., Algebraic K-theory over virtually abelian groups , J. Pure Appl. Algebra 216 (2012), 170183.
[Sau09] Sauer, R., Amenable covers, volume and L 2 -Betti numbers of aspherical manifolds , J. Reine Angew. Math. 636 (2009), 4792.
[SWZ14] Szabó, G., Wu, J. and Zacharias, J., Rohklin dimension for actions of residually finite groups, Preprint (2014), arXiv:1408.6096.
[Szc98] Szczepański, A., Relatively hyperbolic groups , Michigan Math. J. 45 (1998), 611618.
[Weg12] Wegner, C., The K-theoretic Farrell–Jones conjecture for CAT(0)-groups , Proc. Amer. Math. Soc. 140 (2012), 779793.
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Coarse flow spaces for relatively hyperbolic groups

  • A. Bartels (a1)


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