Myopic Tutte polynomials and Khovanov homology in ℝP³

@misc{boyle2026myopic,
  title = {{Myopic Tutte polynomials and Khovanov homology in $\mathbbRP^3$}},
  author = {Keegan Boyle and Dean Spyropoulos},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.40122},
  eprint = {2609.40122},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.40122},
}

TY  - UNPB
TI  - Myopic Tutte polynomials and Khovanov homology in ℝP^3
AU  - Keegan Boyle
AU  - Dean Spyropoulos
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.40122
UR  - https://arxiv.org/abs/2609.40122
AB  - We present a "myopic" Tutte polynomial for graphs on ℝP^2 which takes only nullhomologous spanning subgraphs as input. It recovers the generalized Krushkal polynomial and Drobotukhina's analogue of the Jones polynomial for alternating, nullhomologous links in ℝP^3. We use this myopic Tutte polynomial to prove an analogue of the Kauffman-Murasugi-Thistlethwaite Theorem, relating the Jones polynomial of an alternating link to certain refinements of the crossing number. Finally, we construct a spanning tree model for the Khovanov homology of nullhomologous links, mirroring work by Champanerkar-Kofman and Wehrli for links in S^3. For alternating links, we use our model to prove that the Khovanov homology in ℤ/2ℤ coefficients is determined entirely by the Jones polynomial and signatures of the link.
ER  -