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Results tagged with pseudo-holomorphic-curves
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user 10839
2
votes
Clarification on the ”neck stretching” applied to the base space of a Lefschetz fibration
For a start, the base of your Lefschetz fibration had better be
a Riemann surface, or else it won't have any pseudoholomorphic sections for
generic J (see for example Kruglikov's paper https://link.sp …
- 7,005
9
votes
How not to use J-holomorphic curves
One classic thing to do is to take a sequence of holomorphic curves with a tangency condition and assume that the tangency condition still holds in the limit: if the limit is a multiple cover with a b …
- 7,005
7
votes
Accepted
Pseudo-holomorphic disk which is constant along boundary
Extend $u$ to get a $C^1$ pseudoholpmorphic map defined on $\mathbb{C}$ by setting $u$ constant outside the unit disc. It's $C^1$ because you know the derivative of $u$ along the unit circle vanishes …
- 7,005
5
votes
Accepted
Question on Gromov-Witten invariants when $A=0$
In this case, the J-holomorphic curves are all constant, so the
evaluation pseudocycle is the tridiagonal $\{(x,x,x) : x\in
M\}$. You take cycles $A_1,A_2,A_3$ Poincare dual to
$a_1,a_2,a_3$ respectiv …
- 7,005