V2EX fibre bundle

Fibre Bundle

释义 Definition

纤维丛(fibre bundle):数学(尤其是微分几何与拓扑)中的一种结构。它把一个空间(总空间)看作由许多“纤维”(在局部看起来相同的空间)沿着另一个空间(底空间)平滑地“贴合/拼接”而成;在底空间的每个小邻域里,总空间都局部同构于“底空间 × 纤维”。

发音 Pronunciation (IPA)

/fab bndl/ (UK)
/fabr bndl/ (US)

例句 Examples

A cylinder is a simple fibre bundle over a circle.
圆柱面是一个以圆为底空间的简单纤维丛。

In gauge theory, a principal fibre bundle encodes how local symmetries vary across spacetime.
在规范场论中,主纤维丛用来刻画局部对称性如何在时空中变化。

词源 Etymology

fibre 源自拉丁语 fibra,意为“纤维、丝状物”,强调“细长的组成部分”;bundle 来自中古英语 bundle,意为“一捆、一束”。合在一起,“fibre bundle”形象地表达:很多“纤维”按某种规则成束地附着在“底空间”的每一点上。该术语在20世纪拓扑学与几何学发展中固定下来,用于描述“局部像直积、整体可能扭曲”的空间。

相关词 Related Words

文学与经典著作 Literary Works

  • Geometry, Topology and Physics Mikio Nakahara
  • Characteristic Classes John Milnor & James D. Stasheff
  • Differential Forms in Algebraic Topology Raoul Bott & Loring W. Tu
  • A Comprehensive Introduction to Differential Geometry Michael Spivak
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