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On the virtual cohomological dimensions
of Coxeter groups


Author: A. N. Dranishnikov
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. M. Bestvina, The virual cohomological dimension of Coxeter groups, Geometric Group Theory Vol 1, LMS Lecture Notes 181, 19-23. MR 94g:20056
  • 2. A.N. Dranishnikov, Boundaries and cohomological dimensions of Coxeter groups, Preprint (1994).
  • 3. A. Dranishnikov, Homological dimension theory, Russian Math. Surveys 43 (1988), 11-63. MR 90e:55003
  • 4. M. Bestvina, G. Mess, The boundary of negatively curved groups, Jorn. of Amer. Math. Soc. 4 (no. 3) (1991), 469-481. MR 93j:20076
  • 5. V.I. Kuzminov, Homological dimension theory, Russian Math. Surveys 23 (5) (1968), 1-45. MR 39:2158
  • 6. M. Davis, Nonpositive curvature and reflection groups, Preprint (1994).
  • 7. K.S. Brown and P.J. Kahn, Homotopy dimension and simple cohomological dimension of spaces, Comment. Math. Helv. 52 (1977), 11-127. MR 55:11251
  • 8. K.S. Brown, Buildings, Springer-Verlag, New York, Berlin, 1989. MR 90e:20001
  • 9. K.S. Brown, Cohomology of groups, Springer-Verlag, New York, Heidelberg, Berlin, 1982. MR 83k:20002
  • 10. R. Bieri, Homological dimension of discrete groups, Queen Mary College, London, 1976. MR 57:6224
  • 11. M. Davis, The cohomology of a Coxeter group with group ring coefficients, Preprint (1995).

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Additional Information

A. N. Dranishnikov
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: dranish@math.ufl.edu

DOI: https://doi.org/10.1090/S0002-9939-97-04106-3
Received by editor(s): January 28, 1995
Additional Notes: The author was partially supported by NSF grant DMS-9500875
Communicated by: James West
Article copyright: © Copyright 1997 American Mathematical Society

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