Invariants of 4-Dimensional 2-Handlebodies from the Temperley-Lieb Category in Positive Characteristic
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909966442430464 |
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| author | Décoppet, Thibault D. Haïoun, Benjamin |
| author_facet | Décoppet, Thibault D. Haïoun, Benjamin |
| contents | We investigate invariants of 4-dimensional 2-handlebodies associated to the Temperley-Lieb category in characteristic $p>2$ and at a primitive fourth root of unity. These invariants depend additionally on a height parameter $n$, and we focus on the case $n=2$. Provided that $p>3$, we show that the height $n=2$ invariant associated to the Temperley-Lieb category at a primitive fourth root of unity vanishes on $\mathbb{C}P^2$, $\overline{\mathbb{C}P}^2$, and $S^2\times S^2$. In particular, it has the potential to detect exotic smooth structures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariants of 4-Dimensional 2-Handlebodies from the Temperley-Lieb Category in Positive Characteristic Décoppet, Thibault D. Haïoun, Benjamin Quantum Algebra Geometric Topology 18M15, 57R56, 57K41 We investigate invariants of 4-dimensional 2-handlebodies associated to the Temperley-Lieb category in characteristic $p>2$ and at a primitive fourth root of unity. These invariants depend additionally on a height parameter $n$, and we focus on the case $n=2$. Provided that $p>3$, we show that the height $n=2$ invariant associated to the Temperley-Lieb category at a primitive fourth root of unity vanishes on $\mathbb{C}P^2$, $\overline{\mathbb{C}P}^2$, and $S^2\times S^2$. In particular, it has the potential to detect exotic smooth structures. |
| title | Invariants of 4-Dimensional 2-Handlebodies from the Temperley-Lieb Category in Positive Characteristic |
| topic | Quantum Algebra Geometric Topology 18M15, 57R56, 57K41 |
| url | https://arxiv.org/abs/2512.14849 |