Arithmeticity, discreteness and volume

  • Gehring F
  • Maclachlan C
  • Martin G
  • et al.
34Citations
Citations of this article
7Readers
Mendeley users who have this article in their library.

Abstract

We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of $PSL(2,{\bold C})$. We then examine certain two-generator groups which arise as extremals in various geometric problems in the theory of Kleinian groups, in particular those encountered in efforts to determine the smallest co-volume, the Margulis constant and the minimal distance between elliptic axes. We establish the discreteness and arithmeticity of a number of these extremal groups, the associated minimal volume arithmetic group in the commensurability class and we study whether or not the axis of a generator is simple.

Cite

CITATION STYLE

APA

Gehring, F. W., Maclachlan, C., Martin, G. J., & Reid, A. W. (1997). Arithmeticity, discreteness and volume. Transactions of the American Mathematical Society, 349(9), 3611–3643. https://doi.org/10.1090/s0002-9947-97-01989-2

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free