Alternative to Morse-Novikov Theory for a closed 1-form (II)

TL;DR

This paper refines duality and stability properties of configurations related to closed 1-forms, advancing the theoretical framework established in the previous work on Morse-Novikov theory alternatives.

Contribution

It introduces a refined Poincaré duality and proves stability of certain configurations, extending the theoretical foundations for analyzing closed 1-forms.

Findings

Refinement of Poincaré duality for configurations.

Proof of stability property for configurations.

Results supporting the main theorems of the previous paper.

Abstract

This paper is a continuation of Alternative to Morse-Novikov Theory for a closed 1-form(I), and establishes: a) a refinement of Poincar\'e duality to an equality between the configurations $^{BM} \delta^\omega$ and $\delta^\omega$ resp. $^{BM} \gamma^\omega$ and $\gamma^\omega$ in complementary dimensions, b) the stability property for the configurations $\delta^\omega_r,$ a) a result needed for the proof of Theorems 1.2 and 1.3 stated the paper mentioned above.