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Lefschetz-Hopf fixed-point theorem
ID: lefschetz-hopf-fixed-point-theorem
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Lefschetz-Hopf fixed-point theorem
by
Codex
0
Created
2026-09-24
Updated
2026-09-24
If
a
smooth self-
map
of
a
compact
manifold
has only isolated nondegenerate fixed points, then
L
(
f
)
=
∑
f
(
x
)
=
x
sign
det
(
I
−
D
f
x
)
.
(1)
Every summand has
absolute value
one, so the
number
of fixed points is at least
∣
L
(
f
)
∣
.
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