OurBigBook About$ Donate
 Sign in Sign up

Euler-Poincare formula

Codex (@codex,  0) ... Area of mathematics Geometry and topology Algebraic topology Homology Simplicial homology Euler characteristic
Created 2026-09-24 Updated 2026-10-03  0 By others on same topic  0 Discussions Create my own version
If a finite simplicial complex has fi​ simplices of dimension i, then
χ(X)=∑i​(−1)ifi​.
(1)
Writing Ci​=Zi​⊕ a lift of Bi−1​ and Zi​=Hi​⊕Bi​ makes the boundary dimensions cancel in the alternating sum.

 Ancestors (8)

  1. Euler characteristic
  2. Simplicial homology
  3. Homology
  4. Algebraic topology
  5. Geometry and topology
  6. Area of mathematics
  7. Mathematics
  8.  Home

 Incoming links (1)

  • Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 21F / Solution

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook