On the virtual cohomological dimensions of Coxeter groups
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- by A. N. Dranishnikov PDF
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Abstract:
We apply Bestvina’s approach of calculation of the virtual cohomological dimension of Coxeter groups. The explicit formula for $vcd_{F}\Gamma$ in terms of cohomological properties of the corresponding complex $K$ is given.References
- Mladen Bestvina, The virtual cohomological dimension of Coxeter groups, Geometric group theory, Vol. 1 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 181, Cambridge Univ. Press, Cambridge, 1993, pp. 19–23. MR 1238512, DOI 10.1017/CBO9780511661860.003
- A.N. Dranishnikov, Boundaries and cohomological dimensions of Coxeter groups, Preprint (1994).
- A. N. Dranishnikov, Homological dimension theory, Uspekhi Mat. Nauk 43 (1988), no. 4(262), 11–55, 255 (Russian); English transl., Russian Math. Surveys 43 (1988), no. 4, 11–63. MR 969565, DOI 10.1070/RM1988v043n04ABEH001900
- Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469–481. MR 1096169, DOI 10.1090/S0894-0347-1991-1096169-1
- V. I. Kuz′minov, Homological dimension theory, Uspehi Mat. Nauk 23 (1968), no. 5 (143), 3–49 (Russian). MR 0240813
- M. Davis, Nonpositive curvature and reflection groups, Preprint (1994).
- Kenneth S. Brown and Peter J. Kahn, Homotopy dimension and simple cohomological dimension of spaces, Comment. Math. Helv. 52 (1977), no. 1, 111–127. MR 438336, DOI 10.1007/BF02567359
- Kenneth S. Brown, Buildings, Springer-Verlag, New York, 1989. MR 969123, DOI 10.1007/978-1-4612-1019-1
- Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York-Berlin, 1982. MR 672956
- Robert Bieri, Homological dimension of discrete groups, Queen Mary College Mathematics Notes, Queen Mary College, Mathematics Department, London, 1976. MR 0466344
- M. Davis, The cohomology of a Coxeter group with group ring coefficients, Preprint (1995).
Additional Information
- A. N. Dranishnikov
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- MR Author ID: 212177
- Email: dranish@math.ufl.edu
- Received by editor(s): January 28, 1995
- Additional Notes: The author was partially supported by NSF grant DMS-9500875
- Communicated by: James West
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1885-1891
- MSC (1991): Primary 20F32, 55M10, 57S30; Secondary 16A60, 20J05, 51K10, 54E45
- DOI: https://doi.org/10.1090/S0002-9939-97-04106-3
- MathSciNet review: 1422863