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Symplectic adjunction formula
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Area of mathematics
Geometry and topology
Differential geometry
Symplectic geometry
Symplectic manifold
Symplectic submanifold
Created
2026-09-28
Updated
2026-10-14
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For
a
connected embedded
symplectic surface
C
in
a
symplectic four-
manifold
,
2
g
(
C
)
−
2
=
C
2
+
K
ω
⋅
C
,
(1)
where
K
ω
=
−
c
1
(
TM
,
J
)
is the symplectic canonical class for any
compatible almost complex structure
.
Ancestors
(8)
Symplectic submanifold
Symplectic manifold
Symplectic geometry
Differential geometry
Geometry and topology
Area of mathematics
Mathematics
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Base-point count for a Lefschetz pencil on a symplectic four-torus
Genus of a symplectic Lefschetz pencil on the complex projective plane
Past exam of the mathematics course of the University of Cambridge
/
2006
/
iii
/
Paper 20
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 146
/
1
/
Solution
Symplectic canonical class
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