V2EX fiber bundle

Fiber Bundle

定义 Definition

fiber bundle(纤维丛/纤维束):在数学(拓扑学、微分几何)中指一种空间结构:整体空间在“局部”看起来像底空间(base space)× 纤维(fiber)的乘积,并通过投影映射把每个点对应到其上方的一条“纤维”。常用于描述“随位置变化的一族空间”。(在生物学/医学语境中也可泛指“纤维束”,即成束的纤维组织,但此处以数学义为主。)

发音 Pronunciation (IPA)

/fabr bndl/

例句 Examples

A vector bundle is a kind of fiber bundle.
向量丛是一种纤维丛。

In gauge theory, principal fiber bundles provide a geometric way to describe how fields vary over spacetime.
在规范理论中,主纤维丛提供了一种几何方式来描述场如何随时空变化。

词源 Etymology

fiber 源自拉丁语 fibra(“纤维、丝状物”);bundle 源自中古英语,意为“捆、束”。作为复合术语 fiber bundle,主要在20世纪的拓扑学与几何学发展中固定下来,用来形象地表达“许多纤维按某种规则成束地附着在底空间之上”的结构。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Topology and Geometry(Glen E. Bredon)
  • The Geometry of Physics: An Introduction(Theodore Frankel)
  • Gauge Fields, Knots and Gravity(John C. Baez & Javier P. Muniain)
  • Differential Topology(Victor Guillemin & Alan Pollack)
  • Foundations of Differential Geometry(Shoshichi Kobayashi & Katsumi Nomizu)
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