A Decomposition Theorem for Cayley Graphs of Picard Group Quotients

  title={A Decomposition Theorem for Cayley Graphs of Picard Group Quotients},
  author={Jason Rosenhouse},
The Picard group is defined as Γ = SL(2,Z[i]); the ring of 2× 2 matrices with Gaussian integer entries and determinant one. We consider certain graphs associated to quotients Γ/Γ(p) where p is a prime congruent to three mod four and Γ(p) is the congruence subgroup of level p. We prove a decomposition theorem on the vertices of these graphs, and use this decomposition to derive upper and lower bounds on their isoperimetric numbers. 

From This Paper

Topics from this paper.
4 Citations
5 References
Similar Papers


Publications referenced by this paper.
Showing 1-5 of 5 references

Spectral Graph Theory, No

  • F.R.K. Chung
  • Regional Conference Series in Mathematics…
  • 1991
1 Excerpt

Algebraic Theory of the Bianchi Groups, Marcel Dekker, Inc

  • B. Fine
  • New York,
  • 1989
2 Excerpts

Integral Matrices

  • M. Newman
  • Pure and Applied Mathematics
  • 1972
1 Excerpt

Similar Papers

Loading similar papers…