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Reduced Khovanov-Rozansky homology

  • David Popović
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Abstract

We introduce a variant of reduced Khovanov-Rozansky homology defined in terms of the variables alpha_1, ..., alpha_{n-1} that correspond to the regions between the strands. We rigorously reestablish several folklore results in terms of our framework, including the equivalence between Khovanov's and Rasmussen's approaches. Furthermore, we show that Rasmussen's chain complex is a free resolution of the Rouquier chain complex.

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Cite

BibTeXRIS
BibTeX
@misc{popovic2026reduced,
  title = {{Reduced Khovanov-Rozansky homology}},
  author = {David Popović},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29747},
  eprint = {2608.29747},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29747},
}
RIS
TY  - UNPB
TI  - Reduced Khovanov-Rozansky homology
AU  - David Popović
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29747
UR  - https://arxiv.org/abs/2608.29747
AB  - We introduce a variant of reduced Khovanov-Rozansky homology defined in terms of the variables alpha_1, ..., alpha_{n-1} that correspond to the regions between the strands. We rigorously reestablish several folklore results in terms of our framework, including the equivalence between Khovanov's and Rasmussen's approaches. Furthermore, we show that Rasmussen's chain complex is a free resolution of the Rouquier chain complex.
ER  -