## Duke Mathematical Journal

### Cohomology at infinity and the well-rounded retract for general linear groups

#### Article information

Source
Duke Math. J., Volume 90, Number 3 (1997), 549-576.

Dates
First available in Project Euclid: 19 February 2004

https://projecteuclid.org/euclid.dmj/1077232814

Digital Object Identifier
doi:10.1215/S0012-7094-97-09015-3

Mathematical Reviews number (MathSciNet)
MR1480546

Zentralblatt MATH identifier
0903.11016

Subjects
Primary: 11F75: Cohomology of arithmetic groups
Secondary: 20G10: Cohomology theory

#### Citation

Ash, Avner; McConnell, Mark. Cohomology at infinity and the well-rounded retract for general linear groups. Duke Math. J. 90 (1997), no. 3, 549--576. doi:10.1215/S0012-7094-97-09015-3. https://projecteuclid.org/euclid.dmj/1077232814

#### References

• [A1] A. Ash, Deformation retracts with lowest possible dimension of arithmetic quotients of self-adjoint homogeneous cones, Math. Ann. 225 (1977), no. 1, 69–76.
• [A2] A. Ash, Cohomology of congruence subgroups $\rm SL(n,\,\bf Z)$, Math. Ann. 249 (1980), no. 1, 55–73.
• [A3] A. Ash, Small-dimensional classifying spaces for arithmetic subgroups of general linear groups, Duke Math. J. 51 (1984), no. 2, 459–468.
• [A4] A. Ash, Galois representations attached to mod $p$ cohomology of $\rm GL(n,\bf Z)$, Duke Math. J. 65 (1992), no. 2, 235–255.
• [AGG] A. Ash, D. Grayson, and P. Green, Computations of cuspidal cohomology of congruence subgroups of $\rm SL(3,\bf Z)$, J. Number Theory 19 (1984), no. 3, 412–436.
• [AM1] A. Ash and M. McConnell, Doubly cuspidal cohomology for principal congruence subgroups of $\rm GL(3,\bf Z)$, Math. Comp. 59 (1992), no. 200, 673–688.
• [AM2] A. Ash and M. McConnell, Experimental indications of three-dimensional Galois representations from the cohomology of $\rm SL(3,\bf Z)$, Experiment. Math. 1 (1992), no. 3, 209–223.
• [BS] A. Borel and J.-P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436–491, with an appendix Arrondissement des variétés à coins, by A. Doudy and L. Hérault.
• [BT] R. Bott and L. W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics, vol. 82, Springer-Verlag, New York, 1982.
• [Br] K. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1982.
• [B] A. Brownstein, Homology of Hilbert modular groups, thesis, Univ. of Michigan, 1987.
• [G] D. Grayson, Reduction theory using semistability, Comment. Math. Helv. 59 (1984), no. 4, 600–634.
• [H] G. Harder, Some results on the Eisenstein cohomology of arithmetic subgroups of $\rm GL\sb n$, Cohomology of arithmetic groups and automorphic forms (Luminy-Marseille, 1989) eds. J.-P. Labesse and J. Schwermer, Lecture Notes in Math., vol. 1447, Springer, Berlin, 1990, pp. 85–153.
• [LS] R. Lee and R. H. Szczarba, On the torsion in $K\sb4(\bf Z)$ and $K\sb5(\bf Z)$, Duke Math. J. 45 (1978), no. 1, 101–129.
• [MM1] R. MacPherson and M. McConnell, Classical projective geometry and modular varieties, Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988) ed. J. I. Igusa, Johns Hopkins Univ. Press, Baltimore, MD, 1989, Proceedings of the JAMI Inaugural Conference, pp. 237–290.
• [MM2] R. MacPherson and M. McConnell, Explicit reduction theory for Siegel modular threefolds, Invent. Math. 111 (1993), no. 3, 575–625.
• [M1] M. McConnell, Classical projective geometry and arithmetic groups, Math. Ann. 290 (1991), no. 3, 441–462.
• [M2] M. McConnell, Cell decompositions of Satake compactifications for $SL(n,\mathbbR)$, preprint.
• [Men] E. Mendoza, Cohomology of $\rm PGL\sb2$ over imaginary quadratic integers, Bonner Mathematische Schriften [Bonn Mathematical Publications], 128, Universität Bonn Mathematisches Institut, Bonn, 1979.
• [S] L. Saper, Tilings and finite energy retractions of locally symmetric spaces, preprint.
• [SV] J. Schwermer and K. Vogtmann, The integral homology of $\rm SL\sb2$ and $\rm PSL\sb2$ of Euclidean imaginary quadratic integers, Comment. Math. Helv. 58 (1983), no. 4, 573–598.
• [Sou1] C. Soulé, The cohomology of $\rm SL\sb3(\bf Z)$, Topology 17 (1978), no. 1, 1–22.
• [Sou2] C. Soulé thèse, Univ. Paris VII.
• [Sto] M. I. Štogrin, Locally quasidensest lattice packings of spheres, Dokl. Akad. Nauk SSSR 218 (1974), 62–65.
• [vGT] B. van Geemen and J. Top, A non-selfdual automorphic representation of $\rm GL\sb 3$ and a Galois representation, Invent. Math. 117 (1994), no. 3, 391–401.
• [V] K. Vogtmann, Rational homology of Bianchi groups, Math. Ann. 272 (1985), no. 3, 399–419.