Is there any documented study of geometry in contemporary primates ? There are many studies of language learning abilities of primates (mostly chimpanzee, bonobo) and studies of tool use, knowledge transmission and number sense.
Are there studies or documented cases of drawing, any form of abstract graphical representation, use of concrete objects as representatives, symbols for other things not present, hints of ideal shapes such as circles or lines, uses of markings or pebbles for counting, etc ?
The less influenced by trainers and observers, the better.
 A: The following is an informal response written by Professor Laurie R. Santos of Yale University.

This is a tricky one, as there's lots of controversy on the specifics
  related to these questions in the field of primate cognition.  On the one hand,
  there is evidence that some primates (chimpanzees and capuchin monkeys) can use
  some kinds of symbolic representations in some situations.  For example, both
  chimpanzees and capuchins can be trained to use tokens to represent different
  numerosities.  Once trained, they can do all kinds of smart things with these
  new symbols-- including adding and subtracting them, and so on.  There's also
  evidence that chimpanzees can understand some spatial symbols, such as using a
  scale model of a room to figure out where a piece of food in a real room is
  hidden.  I think this use of a scale geometric model is actually the best
  evidence for symbol use that's really geometric in nature.  That said, it's
  pretty limited and does appear to require at least some training to get going. 
  To my knowledge, there are not real cases of other spontaneous kinds of
  symbols.  There's nothing like representational drawing in primates (lots of
  very abstract painting, but nothing that would suggest graphical
  representations) or anything like spontaneous use of marking/pebbles for
  counting.  So I guess the upshot is that primates can use symbols sometimes, but
  in very restricted, very scaffolded, and often very limited ways.
Here are also two references that might be of use...
chimpanzee use of scale models:
  http://www.infantcognitiongroup.com/Portals/0/PapersPosters/KuhlmeierEtAl(1999).pdf
capuchin use of symbols:
  http://www.sciencedaily.com/releases/2008/06/080610212404.htm

(ed -- note that the comments below were written about a previous revision of this answer, which was just a promise to ask Prof. Santos! Since the question is currently closed, Pete's only option was to edit this answer.)
A: By following links provided by contributors to the meta-discussion, I have found these two resources of interest:
The Comparative Cognition Society
and the book Animal Spatial Cognition
Reading the rather strait-jacketed Wikipedia article on Animal Cognition, the idea of Cephalopodic Mathematics comes to mind as another pursuit.
