Abstract
The gauge fixing (Gribov) ambiguity on the lattice is investigated in simple models. The global understanding of this phenomenon comes from singer's analysis of the bundle of connections. This bundle in continuum gauge theory is infinite dimensional and of non-trivial topology, however on the lattice it is finite dimensional and tractable. Theoretical expectations from Morse theory are supported by numerical evidence, and the structure of lattice gauge orbit space is displayed. Finally, shortcomings of standard gauge fixing prescriptions are addressed.
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