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Everything about Fiber bundle

Continuous surjection satisfying a local triviality condition

In mathematics, and particularly topology, a fiber bundle is a space that is locally a product space, but globally may have a different topological structure. Specifically, the similarity between a space and a product space is defined using a continuous surjective map, that in small regions of behaves just like a projection from corresponding regions of to The map called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space is known as the total space of the fiber bundle, as the base space, and the fiber. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Fiber bundleA 5-minute orientation
  2. Skim a recent paper: Ptycho-endoscopy on a lensless ultrathin fiber bundle tipInfluential work since 2022
  3. Pick up a classic book: Fibre bundlesThe most-reprinted book on the subject
  4. Read the landmark paper: Structural and mechanical properties of bamboo fiber bundle and fiber/bundle reinforced composites: a reviewCited 273 times
  5. Go sideways: Bundle mapA closely related topic
  6. Go sideways: Section (fiber bundle)A closely related topic

📖 Definitions

Noun Synonym of vascular bundle.

Noun An abstract object in topology where copies of one object are "attached" to every point of another, as hairs or fibers are attached to a hairbrush. Formally, a topological space E (called the total space), together with a topological space B (called the base space), a topological space F (called the fiber), and surjective map π from E to B (called the projection or submersion), such that every point of B has a neighborhood U with π−1(U) homeomorphic to the product space U × F (that is, E looks locally the same as the product space B × F, although its global structure may be quite different).

🗂️ The subject at a glance

  1. History
  2. Formal definition
  3. Examples
  4. Sections
  5. Structure groups and transition functions
  6. Bundle maps
  7. Differentiable fiber bundles
  8. Generalizations

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

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