  When fixing a covariant gauge, most popularly the Landau gauge, on the
lattice one encounters the Neuberger 0/0 problem which prevents one from
formulating a Becchi--Rouet--Stora--Tyutin symmetry on the lattice. Following
the interpretation of this problem in terms of Witten-type topological field
theory and using the recently developed Morse theory for orbifolds, we propose
a modification of the lattice Landau gauge via orbifolding of the gauge-fixing
group manifold and show that this modification circumvents the orbit-dependence
issue and hence can be a viable candidate for evading the Neuberger problem.
Using algebraic geometry, we also show that though the previously proposed
modification of the lattice Landau gauge via stereographic projection relies on
delicate departure from the standard Morse theory due to the non-compactness of
the underlying manifold, the corresponding gauge-fixing partition function
turns out to be orbit independent for all the orbits except in a region of
measure zero.
