The pseudoholomorphic curves we encounter are either orbit cylinders or em- bedded with genus zero, one boundary component, and Fredholm index 2. Such curves are automatically regular.

Abstract: A Fukaya category F (M) of a symplectic manifold M is supposed to be a triangulated A-infinity category whose objects are (some) Lagrangians (with additional structure), morphism spaces are ...

In this paper, we establish nonlinear ellipticity of the equation of contact instantons with Legendrian boundary condition on punctured Riemann surfaces by proving the a priori elliptic coercive ...

Abstract:I will explain a construction of a global Kuranishi chart for the moduli space of stable pseudoholomorphic maps in detail. Afterwards, I will sketch our proof of the (fibre) product formula ...

Novikov ring which has been used as a coefficient over the closed symplectic manifold that when encountered through an extension, Big one, from the ordinary cohomology to the quantum cohomology, then ...

Local normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even in finite dimensions. The proof is inspired by the ...

The counterexamples presented here are the first of this kind for notions of differentiability that satisfy a chain rule. Their context arises naturally from requiring differentiability of crucial ...

To regularize moduli spaces of pseudoholomorphic curves despite an absence of inverse and implicit function theorems, Hofer, Wysocki, and Zehnder (6) show that they are in fact the zero set of ...

The examples include intersection of almost complex manifolds, pseudoholomorphic maps and zero locus of certain harmonic forms.One of the main technical tools is Taubes' notion of "positive cohomology ...

Symplectic vortices are stable field configurations in two-dimensional Yang-Mills-Higgs theory; their gauge equivalence classes provide equivariant analogues of pseudoholomorphic curves in the context ...

Dusa McDuff and Dietmar Salamon will receive the 2017 AMS Leroy P. Steele Prize for Exposition for their book 'J-holomorphic Curves and Symplectic Topology' (AMS Colloquium Publications, 52, 2004 ...