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Euler-Poincare formula
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)
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Area of mathematics
Geometry and topology
Algebraic topology
Homology
Simplicial homology
Euler characteristic
Created
2026-09-24
Updated
2026-10-03
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If
a
finite
simplicial complex
has
f
i
simplices of
dimension
i
, then
χ
(
X
)
=
∑
i
(
−
1
)
i
f
i
.
(1)
Writing
C
i
=
Z
i
⊕
a
lift of
B
i
−
1
and
Z
i
=
H
i
⊕
B
i
makes the boundary
dimensions
cancel in the alternating
sum
.
Ancestors
(8)
Euler characteristic
Simplicial homology
Homology
Algebraic topology
Geometry and topology
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2025
/
ii
/
Paper 4
/
21F
/
Solution
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