An approximation to the Loch Ness monster surface. The monster should really be infinitely long with an infinite number of loops.

A plot of a part of a Loch Ness monster surface.

In mathematics, the Loch Ness monster is a surface with infinite genus but only one end. It appeared named this way already in a 1981 article by Sullivan & Phillips (1981). The surface can be constructed by starting with a plane (which can be thought of as the surface of Loch Ness) and adding an infinite number of handles (which can be thought of as loops of the Loch Ness monster).

See also

• Cantor tree surface
• Jacob's ladder surface

References

• Sullivan, Dennis; Phillips, Anthony (1981), "Geometry of leaves", Topology, 20 (2): 209–218, doi:10.1016/0040-9383(81)90039-2, ISSN 0040-9383, MR 0605659
• Ghys, Étienne (1995), "Topologie des feuilles génériques", Annals of Mathematics, Second Series, 141 (2): 387–422, doi:10.2307/2118526, ISSN 0003-486X, JSTOR 2118526, MR 1324140
• Walczak, Paweł (2004), Dynamics of foliations, groups and pseudogroups, Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series) [Mathematics Institute of the Polish Academy of Sciences. Mathematical Monographs (New Series)], vol. 64, Birkhäuser Verlag, ISBN 978-3-7643-7091-6, MR 2056374
• Arredondo, John A.; Ramírez-Maluendas, Camilo (2017), "On the Infinite Loch Ness monster", Commentationes Mathematicae Universitatis Carolinae, 58 (4): 465–479, arXiv:1701.07151, Bibcode:2017arXiv170107151A, doi:10.14712/1213-7243.2015.227, ISSN 0010-2628