Inverted Habiro Series and its Residues
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918148972740608 |
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| author | Svoboda, Josef |
| author_facet | Svoboda, Josef |
| contents | We study the Gukov--Manolescu (GM) series of knots and the inverted Habiro series (IHS) proposed by S. Park. We give a new formula for IHS in terms of coefficients of the GM series and truncated theta functions. We prove a multiplication formula for IHS, constructing a natural ring, in analogy with work of Habiro. We study the residues of IHS and apply them to Dehn surgery formulas. We also give a curious relation between the asymptotics of the GM series at roots of unity and the Kashaev invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverted Habiro Series and its Residues Svoboda, Josef Geometric Topology Quantum Algebra We study the Gukov--Manolescu (GM) series of knots and the inverted Habiro series (IHS) proposed by S. Park. We give a new formula for IHS in terms of coefficients of the GM series and truncated theta functions. We prove a multiplication formula for IHS, constructing a natural ring, in analogy with work of Habiro. We study the residues of IHS and apply them to Dehn surgery formulas. We also give a curious relation between the asymptotics of the GM series at roots of unity and the Kashaev invariant. |
| title | Inverted Habiro Series and its Residues |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2509.22610 |