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).
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.
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, ISBN978-3-7643-7091-6, 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
January 01, 1970
loch, ness, monster, surface, mathematics, loch, ness, monster, surface, with, infinite, genus, only, appeared, named, this, already, 1981, article, sullivan, phillips, 1981, surface, constructed, starting, with, plane, which, thought, surface, loch, ness, add. 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 amp 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 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 See also editCantor tree surface Jacob s ladder surfaceReferences editSullivan 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 Etienne 1995 Topologie des feuilles generiques Annals of Mathematics Second Series 141 2 387 422 doi 10 2307 2118526 ISSN 0003 486X JSTOR 2118526 MR 1324140 Walczak Pawel 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 Birkhauser Verlag ISBN 978 3 7643 7091 6 MR 2056374 Arredondo John A Ramirez 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 Retrieved from https en wikipedia org w index php title Loch Ness monster surface amp oldid 1081606113, wikipedia, wiki, book, books, library,
