Arnold Conjecture for Clifford Symplectic Pencils

TL;DR

This paper proves a version of the Arnold conjecture for manifolds with Clifford pencils of symplectic structures and divergence-free vector fields, extending previous hyperkähler and three-dimensional results.

Contribution

It generalizes the Arnold conjecture to Clifford symplectic pencils and divergence-free vector fields, broadening the scope of previous hyperkähler and lower-dimensional cases.

Findings

Established the Arnold conjecture for Clifford symplectic pencils

Extended results to both degenerate and non-degenerate cases

Generalized previous work on hyperkähler and three-dimensional cases

Abstract

We establish a version of the Arnold conjecture, both the degenerate and non-degenerate case, for target manifolds equipped with Clifford pencils of symplectic structures and the domains (time-manifolds) equipped with frames of divergence-free vector fields. This result generalizes the original work on the hyperkahler Arnold conjecture by Hohloch, Noetzel and Salamon for three-dimensional time and also the previous work by the authors.