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Two non-semisimple quantum invariants of lens spaces

  • Rhea Palak Bakshi
  • Mitchell Jubeir
  • Quinn T. Kolt
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Abstract

We calculate the chromatic spherical invariant ๐’ฆRep(H)(L(p,q)) of lens spaces $L(p, q)$ for arbitrary finite-dimensional unibalanced, unimodular Hopf algebras H. In the case of the index-2 Nichols Hopf algebra ๐’ฆ2 and q=1, we find that the invariant of $L(p, 1)$ depends only on the parity of p for pโ‰ฅ 1. We also describe the duals ๐’ฎ_โ„(M)* of the admissible skein modules of handlebodies M=Hg and of M=L(p, q) for arbitrary tensor ideals โ„ of a ribbon tensor category. In particular, ๐’ฎ_โ„(L(p, q))* corresponds with cyclic traces on โ„ satisfying a property reminiscent of the modified trace condition.

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Cite

BibTeXRIS
BibTeX
@misc{bakshi2026nonsemisimple,
  title = {{Two non-semisimple quantum invariants of lens spaces}},
  author = {Rhea Palak Bakshi and Mitchell Jubeir and Quinn T. Kolt},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19355},
  eprint = {2610.19355},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19355},
}
RIS
TY  - UNPB
TI  - Two non-semisimple quantum invariants of lens spaces
AU  - Rhea Palak Bakshi
AU  - Mitchell Jubeir
AU  - Quinn T. Kolt
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19355
UR  - https://arxiv.org/abs/2610.19355
AB  - We calculate the chromatic spherical invariant ๐’ฆ_Rep(H)(L(p,q)) of lens spaces $L(p, q)$ for arbitrary finite-dimensional unibalanced, unimodular Hopf algebras H. In the case of the index-2 Nichols Hopf algebra ๐’ฆ_2 and q=1, we find that the invariant of $L(p, 1)$ depends only on the parity of p for pโ‰ฅ 1. We also describe the duals ๐’ฎ_โ„(M)^* of the admissible skein modules of handlebodies M=H_g and of M=L(p, q) for arbitrary tensor ideals โ„ of a ribbon tensor category. In particular, ๐’ฎ_โ„(L(p, q))^* corresponds with cyclic traces on โ„ satisfying a property reminiscent of the modified trace condition.
ER  -