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arXiv · 2501.17809

Morse-Novikov homology and $β$-critical points

Adrien Currier
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Abstract

Given a manifold $M$, some closed $β\inΩ^1(M)$ and a map $f\in C^\infty(M)$, a $β$-critical point is some $x\in M$ such that $d_βf_{x}=0$ for the Lichnerowicz derivative $d_β$. In this paper, we will give a lower bound for the number of $β$-critical points of index $i$ of a $β$-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. 2025-02-12. Morse-Novikov homology and $β$-critical points. https://arxiv.org/abs/2501.17809

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