AbstractWe give a detailed proof of the homological Arnold conjecture for nondegenerate periodic Hamiltonians on general closed symplectic manifolds M via a direct Piunikhin–Salamon–Schwarz morphism. Our constructions are based on a coherent polyfold description for moduli spaces of pseudoholomorphic curves in a family of symplectic manifolds degenerating from $${{\mathbb {C}}{\mathbb {P}}}^1\times M$$
C
P
1
×
M
to $${{\mathbb {C}}}^+ \times M$$
C
+
×
M
and $${{\mathbb {C}}}^-\times M$$
C
-
×
M
, as developed by Fish–Hofer–Wysocki–Zehnder as part of the Symplectic Field Theory package. To make the paper self-contained we include all polyfold assumptions, describe the coherent perturbation iteration in detail, and prove an abstract regularization theorem for moduli spaces with evaluation maps relative to a countable collection of submanifolds. The 2011 sketch of this proof was joint work with Peter Albers, Joel Fish.
Penrose Transform on <i>D</i>-Modules, Moduli Spaces and Field Theory
