Skein reduction and stabilization for the odd Khovanov spectra of T(2,m)sqcup T(2,n)

@misc{kar2026skein,
  title = {{Skein reduction and stabilization for the odd Khovanov spectra of $T(2,m)\sqcup T(2,n)$}},
  author = {Krishnendu Kar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40245},
  eprint = {2610.40245},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40245},
}

TY  - UNPB
TI  - Skein reduction and stabilization for the odd Khovanov spectra of T(2,m)sqcup T(2,n)
AU  - Krishnendu Kar
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40245
UR  - https://arxiv.org/abs/2610.40245
AB  - For split links the even Khovanov spectrum is a smash product of the spectra of the pieces; the odd one is not. For T(2,m)sqcup T(2,n) we show that the odd spectrum is, in each quantum grading, a wedge of spheres and copies of a suspension of ℂℙ^2. Using the skein cofiber sequence at the level of spectra, we prove that for fixed q−m−n the number of these copies is determined by finitely many small links and stabilizes for large m and n. The ℂℙ^2 summand of T(2,3)sqcup T(2,3), due to Schütz and Rajapakse, persists in quantum grading m+n+8 for all m,n≥3. We conjecture that the number of copies of ℂℙ^2 equals the number of copies of ℝℙ^2∧ℝℙ^2 in the even spectrum.
ER  -