  We construct a smooth compact n-dimensional manifold Y with one point
singularity such that all its Lipschitz homotopy groups are trivial, but
Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space
W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz
(n-1)-connected, then Lipschitz mappings Lip(X,Y) are dense in N^{1,p}(X,Y)
whenever the Nagata dimension of X is bounded by n and the space X supports the
p-Poincare inequality.
