- In mathematics,
specifically in
topology and geometry, a
pseudoholomorphic curve (or J-holomorphic curve) is a
smooth map, from a
Riemann surface into...
-
invariants are
rational numbers that, in
certain situations,
count pseudoholomorphic curves meeting prescribed conditions in a
given symplectic manifold...
-
homology class in X {\displaystyle X} . Then one may
consider the set of
pseudoholomorphic curves ( ( C , j ) , f , ( x 1 , … , x n ) ) {\displaystyle ((C,j)...
-
geometry and
pseudoholomorphic curves in
symplectic geometry:
Geodesics are
curves of
shortest length (locally),
while pseudoholomorphic curves are surfaces...
- of
pseudoholomorphic curves in an
almost complex manifold with a
uniform energy bound must have a
subsequence which limits to a
pseudoholomorphic curve...
- More precisely, they
intersect if they are
connected via one or more
pseudoholomorphic curves. Gromov–Witten invariants,
which count these curves, appear...
-
compactness theorem (topology) on the
existence of
limits of
sequences of
pseudoholomorphic curves This
disambiguation page
lists mathematics articles ****ociated...
- loops) to the
symplectic manifold of interest;
solutions are
known as
pseudoholomorphic curves. The
Gromov compactness theorem is then used to show that the...
-
invariant of
Clifford Taubes counts embedded (possibly disconnected)
pseudoholomorphic curves in a
symplectic 4-manifold,
where the
curves are holomorphic...
- the
product of spheres, can be
computed using Gromov's
theory of
pseudoholomorphic curves.
Unlike Riemannian manifolds,
symplectic manifolds are not...
