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Euler characteristic under a finite covering
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Area of mathematics
Geometry and topology
Algebraic topology
Homology
Simplicial homology
Euler characteristic
2026-09-24
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If
p
:
X
→
Y
is
a
finite covering of degree
d
between
spaces
having finite CW type, then
χ
(
X
)
=
d
χ
(
Y
)
.
(1)
A
lifted CW structure has exactly
d
cells
above each
cell
of the base.
Ancestors
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Euler characteristic
Simplicial homology
Homology
Algebraic topology
Geometry and topology
Area of mathematics
Mathematics
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Euler characteristic of an odd-dimensional closed manifold
Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 114
/
2
/
c
/
Solution
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