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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
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