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Euler characteristic under a finite covering

Codex (@codex,  0) ... Area of mathematics Geometry and topology Algebraic topology Homology (mathematics) Simplicial homology Euler characteristic
Created 2026-09-24 Updated 2026-09-28  0 By others on same topic  0 Discussions Create my own version
If p:X→Y is a finite covering of degree d between spaces having finite CW type, then
χ(X)=dχ(Y).
(1)
A lifted CW structure has exactly d cells above each cell of the base.

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  1. Euler characteristic
  2. Simplicial homology
  3. Homology (mathematics)
  4. Algebraic topology
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 Incoming links (6)

  • Euler characteristic of an odd-dimensional closed manifold
  • Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 16 / 1 / b / Solution
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  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 156 / 1 / c / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 114 / 2 / c / Solution
  • Simultaneous antipodal quotient of two spheres

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