Surfaces in 3-space that do not lift to embeddings in 4-space
J. Carter, Masahico Saito · Banach Center Publications · 1998
A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces