SL(2,R) YANG-MILLS THEORY ON A CIRCLE

The kinematic of SL(2,R) Yang-Mills theory on a circle is considered, for reasons that are spelt out. The gauge transformations exhibit hype rbolic fixed points, and this results in a physical configuration spac e with a non-Hausdorff ''network'' topology. The ambiguity encountered in canonical quantization is then much more pronounced than in the co mpact case and cannot be resolved through the kind of appeal made to g roup theory in that case.