- Y. Ando. "Fold-Maps and the Space of Base Point Preserving Maps of Spheres." J. Math. Kyoto Univ. 41 (2002), 691–735.
- Y. Ando. "Existence Theorems of Fold Maps." Japan J. Math. 30 (2004), 29–73.
- V. I. Arnol'd. "Plane Curves, Their Invariants, Perestroikas and Classifications." Advances in Soviet Math. 21 (1994), 33–91.
- V. I. Arnol'd. Topological Invariants of Plane Curves and Caustics, University Lecture Series, 5. Providence, RI: AMS, 1994.
- S. J. Blank. "Extending Immersions of the Circle." PhD diss., Brandeis University, 1967.
- D. J. R. Chillingworth. "Winding Number on Surfaces, I." Math. Ann. 196 (1972), 218–249.
- Y. Eliashberg. "On Singularities of Folding Type." Math. USSR-Izv. 4 (1970), 1119–1134.
- Y. Eliashberg and N. Mishaev. Introduction to the h-Principle, Graduate Studies in Mathematics, 48. Providence, RI: AMS, 2002.
- M. Golubitsky and V. Guillemin. Stable Mappings and Their Singularities. Berlin: Springer-Verlag, 1976.
- D. Hacon, C. Mendes de Jesus, and M. C. Romero Fuster. "Topological Invariants of Stable Maps from a Surface to the Plane from a Global Viewpoint." In Real and Complex Singularities, 227–235, Lecture Notes in Pure and Appl. Math. 232. New York: Dekker, 2003.
- L. Kauffman. "Planar Surface Immersions." Illinois J. Math. 23 (1979), 648–665.
- I. P. Malta, N. C. Saldanha, and C. Tomei. Geometria e análise numérica de funcões do plano no plano. 19 Colóquio Brasileiro de Matemática, IMPA, 1993.
- C. Mendes de Jesus and M. C. Romero Fuster. "Bridges, Channels and Arnold's Invariants for Generic Plane Curves." Topology Appl. 125:3 (2002), 505–524.
- T. Ohmoto and F. Aicardi. "First Order Local Invariants of Apparent Contours." Topology 45:1 (2006), 27–45.
- S. F. Troyer. "Extending a Boundary Immersion to the Disk with n Holes." PhD diss., Northeastern University, 1973.
- O. Saeki. "Fold Maps on 4-Manifolds." Comment. Math. Helv. 78 (2003), 627–647.
- K. Sakuma. "On the Topology of Simple Fold Maps." Tokyo J. Math. 17 (1994), 21–31.
- W. H. Whitney. "On Regular Closed Curves in the Plane." Comp. Math. 4 (1937), 276–284.
- M. Yamamoto. "Immersions of Surfaces with Boundary into the Plane." Pacific J. Math. 212 (2003), 371–376.
Fold Maps from the Sphere to the Plane
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