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单词 Fiber sum
释义

Fiber sum

中文百科

连通和 Connected sum

(重定向自Fiber sum)

在数学里,尤其是在拓扑学里,连通和的运算是指一于流形上的几何改变。其效果为将两个给定的流形于各个选定的点附近连接起来。此一建构在闭曲面分类上有着关键性的角色。

更一般地,也可以将流形和其子流形连接起来;此一广义化通常称为纤维和。另外还有在结上之连通和的一相关概念,其称为结和或结的复合

英语百科

Connected sum 连通和

(重定向自Fiber sum)
Illustration of connected sum.
 Consider disjoint planar projections of each knot.
Find a rectangle in the plane where one pair of sides are arcs along each knot but is otherwise disjoint from the knots.
Now join the two knots together by deleting these arcs from the knots and adding the arcs that form the other pair of sides of the rectangle.

In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classification of closed surfaces.

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更新时间:2025/6/17 14:47:24