Generic singularities of symplectic and quasi-symplectic immersions

TL;DR

This paper develops a comprehensive set of invariants for classifying singularities of immersed submanifolds in symplectic manifolds at generic double points, advancing understanding of their local geometric structure.

Contribution

It introduces a complete system of invariants for singularity classification of symplectic and quasi-symplectic immersions, filling a gap in the geometric theory.

Findings

Constructed invariants for singularity classification

Applicable to generic double points in symplectic manifolds

Provides a framework for understanding local singularities

Abstract

For any k<2n we construct a complete system of invariants in the problem of classifying singularities of immersed k-dimensional submanifolds of a symplectic 2n-manifold at a generic double point.