  The question about the existence of a structural glass transition in two
dimensions is studied using mode coupling theory (MCT). We determine the
explicit d-dependence of the memory functional of mode coupling for
one-component systems. Applied to two dimensions we solve the MCT equations
numerically for monodisperse hard discs. A dynamic glass transition is found at
a critical packing fraction phi_c^{d=2} = 0.697 which is above phi_c^{d=3} =
0.516 by about 35%. phi^d_c scales approximately with phi^d_{\rm rcp} the value
for random close packing, at least for d=2, 3. Quantities characterizing the
local, cooperative 'cage motion' do not differ much for d=2 and d=3, and we
e.g. find the Lindemann criterion for the localization length at the glass
transition. The final relaxation obeys the superposition principle, collapsing
remarkably well onto a Kohlrausch law. The d=2 MCT results are in qualitative
agreement with existing results from MC and MD simulations. The mean squared
displacements measured experimentally for a quasi-two-dimensional binary system
of dipolar hard spheres can be described satisfactorily by MCT for monodisperse
hard discs over four decades in time provided the experimental control
parameter Gamma (which measures the strength of dipolar interactions) and the
packing fraction phi are properly related to each other.
