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A Topological Quantum Field Theory for Representation Varieties of Torus Links

  • Enrique Aycart-Maldonado
  • Alejandro Calleja
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Abstract

We construct a Topological Quantum Field Theory (TQFT) that computes the virtual classes of G-representation varieties associated with the fundamental group of a torus link complement. Following the framework established by González-Prieto, Logares and Muñoz for G-representation varieties of surface groups, we introduce a suitable bordism whose iteration enables a recursive topological evaluation of these virtual classes. Via this TQFT, we explicitly compute the virtual class of these varieties for the groups G=AGL1(ℂ) and G=SL2(ℂ).

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Cite

BibTeXRIS
BibTeX
@misc{aycartmaldonado2026topological,
  title = {{A Topological Quantum Field Theory for Representation Varieties of Torus Links}},
  author = {Enrique Aycart-Maldonado and Alejandro Calleja},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23644},
  eprint = {2610.23644},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23644},
}
RIS
TY  - UNPB
TI  - A Topological Quantum Field Theory for Representation Varieties of Torus Links
AU  - Enrique Aycart-Maldonado
AU  - Alejandro Calleja
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23644
UR  - https://arxiv.org/abs/2610.23644
AB  - We construct a Topological Quantum Field Theory (TQFT) that computes the virtual classes of G-representation varieties associated with the fundamental group of a torus link complement. Following the framework established by González-Prieto, Logares and Muñoz for G-representation varieties of surface groups, we introduce a suitable bordism whose iteration enables a recursive topological evaluation of these virtual classes. Via this TQFT, we explicitly compute the virtual class of these varieties for the groups G=AGL_1(ℂ) and G=SL_2(ℂ).
ER  -