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crosscap number
Author: Marian Olejar, Jr. Created: Oct/03/2006 Last edit: Oct/03/2006
other names: nonorientable genus
topology: Let's have nonorientable surface. The crosscap number is defined as the number of Möbius bands one must attach to the sphere to obtain its homeomorphism type. Usually denoted `N_k, k>=1`, where k is the crosscap number. `N_0` means the orientable 2-sphere. graph theory: The crosscap number of the graph G is defined as the smallest number k such that G imbeds in the surface `N_k`. The denotation is `bar gamma(G)`. See also: genus, orientable genus, orientable surface, Cite this article as: Marian Olejar, Jr.: crosscap number from VeryPrime's Dictionary of mathematics Link to this page: http://www.veryprime.com/dict/crosscap_number.php |