Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Martinez, Thomas C., Tyler, Matthew J.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214305744