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Crosscap number : ウィキペディア英語版
Crosscap number
In the mathematical field of knot theory, the crosscap number of a knot ''K'' is the minimum of
:1 - \chi(S), \,
taken over all compact, connected, non-orientable surfaces ''S'' bounding ''K''; here \chi is the Euler characteristic. The crosscap number of the unknot is zero, as the Euler characteristic of the disk is one.
==Examples==

*The crosscap number of the trefoil knot is 1, as it bounds a Möbius strip and is not trivial.
*The crosscap number of a torus knot was determined by M. Teragaito.
The formula for the knot sum is
:C(k_1)+C(k_2)-1 \leq C(k_1 \# k_2) \leq C(k_1)+C(k_2). \,

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Crosscap number」の詳細全文を読む



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