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arXiv · 2501.17809

Morse-Novikov homology and $\beta$-critical points

Adrien Currier
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Abstract

Given a manifold $M$, some closed $\beta\in\Omega^1(M)$ and a map $f\in C^\infty(M)$, a $\beta$-critical point is some $x\in M$ such that $d_\beta f_{x}=0$ for the Lichnerowicz derivative $d_\beta$. In this paper, we will give a lower bound for the number of $\beta$-critical points of index $i$ of a $\beta$-Morse function $f$ in terms of the Morse-Novikov homology, and we generalize this result to generating functions (quadratic at infinity). We also give an application to the detection of essential Liouville chords of a set length. These are a type of chords that appear in locally conformally symplectic geometry as even-dimensional analogues to Reeb chords.

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Adrien Currier. 2025-01-29. Morse-Novikov homology and $\beta$-critical points. https://arxiv.org/abs/2501.17809

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