Morse-Novikov homology and $β$-critical points
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916609729232896 |
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| author | Currier, Adrien |
| author_facet | Currier, Adrien |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Morse-Novikov homology and $β$-critical points Currier, Adrien Symplectic Geometry 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. |
| title | Morse-Novikov homology and $β$-critical points |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2501.17809 |