Odd-symplectic forms via surgery and minimality in symplectic dynamics

TL;DR

The paper constructs an infinite family of odd-symplectic forms on the 3-sphere that cannot be connected to the standard contact structure via symplectic cobordisms, addressing questions in symplectic dynamics.

Contribution

It introduces new examples of odd-symplectic forms on the 3-sphere that challenge existing assumptions about symplectic cobordisms and minimal characteristic flows.

Findings

Constructed infinite family of odd-symplectic forms on S^3

Showed these forms do not admit symplectic cobordisms to standard contact structure

Provided insights into minimal characteristic flows in symplectic dynamics

Abstract

We construct an infinite family of odd-symplectic forms (also known as Hamiltonian structures) on the 3-sphere that do not admit a symplectic cobordism to the standard contact structure on the 3-sphere. This answers in the negative a question raised by Joel Fish motivated by the search for minimal characteristic flows.