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Cobordism
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Mathematics
Area of mathematics
Geometry and topology
2026-10-03
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A
cobordism
from
a
closed oriented
n
-
manifold
X
0
to
X
1
is
a
compact oriented
(
n
+
1
)
-
manifold
W
whose oriented boundary is
−
X
0
⊔
X
1
.
Table of contents
One-handle cobordism from a disjoint union to a connected sum
Cobordism
One-handle cobordism from a disjoint union to a connected sum
0
0
0
Cobordism
Start with
(
X
0
⊔
X
1
)
×
[
0
,
1
]
and attach an
(
n
+
1
)
-dimensional one-
handle
D
1
×
D
n
to one
n
-ball in each component of its outgoing boundary. The new outgoing boundary is
X
0
#
X
1
, so this is
a
cobordism
from
X
0
⊔
X
1
to their
connected sum
.
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Geometry and topology
Area of mathematics
Mathematics
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Cobordism
by
Wikipedia Bot
1
View more
Cobordism
is
a
concept
from the
field
of
topology
, particularly in
algebraic topology
, that studies the relationships between
manifolds
. In simple terms,
cobordism
provides
a
way to classify
manifolds
based on their boundaries and their relationships to each other.
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