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Miklós Schweitzer
2018 Miklós Schweitzer
11
11
Part of
2018 Miklós Schweitzer
Problems
(1)
Parallelizable manifolds
Source: Miklós Schweitzer 2018 P11
11/18/2018
We call an
m
m
m
-dimensional smooth manifold parallelizable if it admits
m
m
m
smooth tangent vector fields that are linearly independent at all points. Show that if
M
M
M
is a closed orientable
2
n
2n
2
n
-dimensional smooth manifold of Euler characteristic
0
0
0
that has an immersion into a parallelizable smooth
(
2
n
+
1
)
(2n+1)
(
2
n
+
1
)
-dimensional manifold
N
N
N
, then
M
M
M
is itself parallelizable.
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