Duke Mathematical Journal

The cohomology of a Coxeter group with group ring coefficients

Michael W. Davis

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Article information

Duke Math. J., Volume 91, Number 2 (1998), 297-314.

First available in Project Euclid: 19 February 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 20J05: Homological methods in group theory 57M07: Topological methods in group theory


Davis, Michael W. The cohomology of a Coxeter group with group ring coefficients. Duke Math. J. 91 (1998), no. 2, 297--314. doi:10.1215/S0012-7094-98-09113-X. https://projecteuclid.org/euclid.dmj/1077232080

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  • [Be1] M. 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.
  • [Be2] M. Bestvina, Local homology properties of boundaries of groups, Michigan Math. J. 43 (1996), no. 1, 123–139.
  • [BB] M. Bestvina and N. Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997), no. 3, 445–470.
  • [B] N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968.
  • [Br] K. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1982.
  • [BFMW] J. Bryant, S. C. Ferry, W. Mio, and S. Weinberger, Topology of homology manifolds, Ann. of Math. (2) 143 (1996), no. 3, 435–467.
  • [CD] R. Charney and M. W. Davis, The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold, Pacific J. Math. 171 (1995), no. 1, 117–137.
  • [D1] M. W. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. (2) 117 (1983), no. 2, 293–324.
  • [D2]1 M. W. Davis, Erratum: “The homology of a space on which a reflection group acts”, Duke Math. J. 56 (1988), no. 1, 221.
  • [D2]2 M. W. Davis, The homology of a space on which a reflection group acts, Duke Math. J. 55 (1987), no. 1, 97–104.
  • [D3] M. W. Davis, Nonpositive curvature and reflection groups, in Handbook of Geometric Topology, Elsevier, Amsterdam, to appear.
  • [DH] M. W. Davis and J.-C. Hausmann, Aspherical manifolds without smooth or PL structure, Algebraic topology (Arcata, CA, 1986), Lecture Notes in Math., vol. 1370, Springer, Berlin, 1989, pp. 135–142.
  • [DL] W. Dicks and I. J. Leary, On subgroups of Coxeter groups, in Proc. LMS Durham Symposium on Geometry and Cohomology in Group Theory, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, to appear.
  • [Dr] A. D. Dranishnikov, On the virtual cohomological dimensions of Coxeter groups, Proc. Amer. Math. Soc. 125 (1997), no. 7, 1885–1891.
  • [Fa] F. T. Farrell, Poincaré duality and groups of type $\rm (FP)$, Comment. Math. Helv. 50 (1975), 187–195.
  • [F] S. Ferry, Remarks on Steenrod homology, Novikov conjectures, index theorems and rigidity, Vol. 2 (Oberwolfach, 1993) eds. S. Ferry, A. Ranicki, and J. Rosenberg, London Math. Soc. Lecture Note Ser., vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 148–166.
  • [Me] G. Mess, Examples of Poincaré duality groups, Proc. Amer. Math. Soc. 110 (1990), no. 4, 1145–1146.
  • [M] G. Moussong, Hyperbolic Coxeter groups, Ph.D. thesis, The Ohio State University, 1988.
  • [W] C. T. C. Wall, Finiteness conditions for $\rm CW$-complexes, Ann. of Math. (2) 81 (1965), 56–69.

See also

  • See also: Michael W. Davis. Correction to “The cohomology of a Coxeter group with group ring coefficients”. Duke Math. J. Vol. 95, No. 3 (1998), pp. 635–635.