Toric Richardson Varieties and Slice Links

@misc{martinez2026toric,
  title = {{Toric Richardson Varieties and Slice Links}},
  author = {Thomas C. Martinez and Matthew J. Tyler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28536},
  eprint = {2609.28536},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28536},
}

TY  - UNPB
TI  - Toric Richardson Varieties and Slice Links
AU  - Thomas C. Martinez
AU  - Matthew J. Tyler
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.28536
UR  - https://arxiv.org/abs/2609.28536
AB  - For type A braid varieties, including Richardson varieties and positroid varieties, we prove that the standard torus has a dense orbit exactly when the associated link is smoothly slice. More generally, we relate the smooth slice genus to the codimension of a generic standard-torus orbit. For knots, this codimension equals twice the slice genus. We also characterize algebraic tori among open affine Richardson varieties and positroid patches by 2-crown avoidance in their Bruhat intervals. Finally, positroid links have equal Seifert and slice genera, so a positroid link is smoothly slice exactly when it is an unlink.
ER  -