deck transformation

复迭变换

Geometry & Topology · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: covering transformation

Translation evidence: Literature usage

Meaning in context

A homeomorphism of a covering's total space E satisfying p composed with that homeomorphism equals p.

复迭空间总空间 EE 的同胚 hh，满足 p∘h=pp\circ h=p。

Example

Integer translations are deck transformations of R→S1\mathbb R\to S^1.

Usage and distinctions

A deck transformation must preserve the projection, not just permute fibers by an arbitrary bijection.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Allen Hatcher — Algebraic Topology§1.3, Deck Transformations and Group Actions, printed p. 70 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第15周12月19日，主要概念：复迭变换 · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.