Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3643
Articles: 2'487'895
Articles rated: 2609

28 March 2024
 
  » arxiv » 0909.0062

 Article overview


Fundamental domains for congruence subgroups of SL2 in positive characteristic
Lisa Carbone ; Leigh Cobbs ; Scott H. Murray ;
Date 1 Sep 2009
AbstractMorgenstern ([M]) claimed to have constructed fundamental domains for congruence subgroups of the lattice group Gamma=PGL_2(F_q[t]), and subgraphs providing the first known examples of linear families of bounded concentrators. His method was to construct the fundamental domain for a congruence subgroup as a ’ramified covering’ of the fundamental domain for Gamma on the Bruhat-Tits tree X of G=PGL_2(F_q((t^-1))). We prove that Morgenstern’s constructions do not yield the desired ramified coverings, and in particular yield graphs that are not connected in characteristic 2. It follows that Morgenstern’s graphs cannot be quotient graphs by the action of congruence subgroups on the Bruhat-Tits tree. Moreover, subgraphs of Morgenstern’s graphs which he claims to be expanders are also not connected.
We clarify the construction of Morgenstern and we prove that his full graphs are connected only in odd characteristic. We also repair his constructions of ramified coverings. We construct fundamental domains for congruence subgroups of SL_2(F_q[t]) and PGL_2(F_q[t]) as ramified coverings, and we give explicit graphs of groups for a number of congruence subgroups. We thus provide new families of graphs whose level 0 - 1 subgraphs potentially have the expansion properties claimed by Morgenstern.
Source arXiv, 0909.0062
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser claudebot






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica