  Kuranishi structures were introduced in the 1990s by Fukaya and Ono for the
purpose of assigning a virtual cycle to moduli spaces of pseudoholomorphic
curves that cannot be regularized by geometric methods. Their core idea was to
build such a cycle by patching local finite dimensional reductions. The first
sections of this paper discuss topological, algebraic and analytic challenges
that arise in this program.
  We then develop a theory of Kuranishi atlases and cobordisms that
transparently resolves these challenges, for simplicity concentrating on the
case of trivial isotropy. In this case, we assign to a cobordism class of
additive weak Kuranishi atlases both a virtual moduli cycle (VMC - a cobordism
class of smooth manifolds) and a virtual fundamental class (VFC - a Cech
homology class). We moreover show that such Kuranishi atlases exist on simple
Gromov-Witten moduli spaces and develop the technical results in a manner that
easily transfers to more general settings.
