On the existence of spines for Q-rank 1 groups

  title={On the existence of spines for Q-rank 1 groups},
  author={Dan Yasaki},
Let X = Γ\G/K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has Q-rank 1, we construct Γ-equivariant deformation retractions of D = G/K onto a set D0. We prove that D0 is a spine, having dimension equal to the virtual cohomological dimension of Γ. In fact, there is a (k − 1)-parameter family of such deformation retractions, where k is the number of Γ-conjugacy classes of rational parabolic subgroups of G. The construction of the spine also gives a way to… CONTINUE READING

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
7 Extracted Citations
27 Extracted References
Similar Papers

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 27 references

Continuous Cohomology

  • A. Borel, N. Wallach
  • Discrete Subgroups, and Representations of…
  • 2000
Highly Influential
5 Excerpts

Small-dimensional classifying spaces for arithmetic subgroups of general linear groups

  • A. Ash
  • Duke Math. J. 51
  • 1984
Highly Influential
4 Excerpts

Corners and arithmetic groups

  • A. Borel, J.-P. Serre
  • Comment. Math. Helv. 48
  • 1973
Highly Influential
10 Excerpts

Explicit reduction theory for Siegel modular threefolds

  • R. MacPherson, M. McConnell
  • Invent. Math. 111
  • 1993
Highly Influential
4 Excerpts

Rational homology of Bianchi groups

  • K. Vogtmann
  • Math. Ann. 272
  • 1985
Highly Influential
4 Excerpts

Cohomology of PGL2 over imaginary quadratic integers

  • E. R. Mendoza
  • Bonner Math. Schriften 128, Univ. Bonn
  • 1979
Highly Influential
4 Excerpts

Lectures on Advanced Analytic Number Theory

  • C. L. Siegel
  • Notes by S. Raghavan. Tata Inst. Fund. Res…
  • 1965
Highly Influential
5 Excerpts

Explicit reduction of SU(2

  • D. Yasaki
  • 1; Z[i]). Preprint
  • 2005
2 Excerpts

Similar Papers

Loading similar papers…