  We find a consistent formulation of the constraints of Quantum Gravity with a
cosmological constant in terms of the Ashtekar new variables in the connection
representation, including the existence of a state that is a solution to all
the constraints. This state is related to the Chern-Simons form constructed
from the Ashtekar connection and has an associated metric in spacetime that is
everywhere nondegenerate. We then transform this state to the loop
representation and find solutions to all the constraint equations for
intersecting loops. These states are given by suitable generalizations of the
Jones knot polynomial for the case of intersecting knots. These are the first
physical states of Quantum Gravity for which an explicit form is known both in
the connection and loop representations. Implications of this result are also
discussed.
