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We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenows in the (strong) positive. As a second main result, we give simple and complete characterizations of link diagrams with quasipositive canonical surface (the surface produced by Seiferts algorithm). As applications, we determine which prime knots up to 13 crossings are strongly quasipositive, and we confirm the following conjecture for knots that have a canonical surface realizing their genus: a knot is strongly quasipositive if and only if the Bennequin inequality is an equality.
We give a new, conceptually simpler proof of the fact that knots in $S^3$ with positive L-space surgeries are fibered and strongly quasipositive. Our motivation for doing so is that this new proof uses comparatively little Heegaard Floer-specific mac
We discuss when homogeneous quasipositive links are positive. In particular, we show that a homogeneous diagram of a quasipositive link whose number of Seifert circles is equal to the braid index is a positive diagram.
Every $L$-space knot is fibered and strongly quasi-positive, but this does not hold for $L$-space links. In this paper, we use the so called H-function, which is a concordance link invariant, to introduce a subfamily of fibered strongly quasi-positiv
For a positive braid link, a link represented as a closed positive braids, we determine the first few coefficients of its HOMFLY polynomial in terms of geometric invariants such as, the maximum euler characteristics, the number of split factors, and
We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of positive braid links, in terms of their crossing number. The same braid-theoretic technique, combined with Ozsvath, Stipsicz, and Szabos Upsilon invarian