Homayun Karimi

On knots that divide ribbon knotted surfaces

Hans U. Boden, Ceyhun Elmacioglu, Anshul Guha, Homayun Karimi et autres

Abstract We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a knot K, the minimum genus of a …

ca, us, gb, sg (code pays fourni par la source)

Concordance invariants of null-homologous knots in thickened surfaces

Hans U. Boden, Homayun Karimi

Using the Gordon-Litherland pairing, one can define invariants (signature, nullity, determinant) for ${\mathbb Z}/2$ null-homologous links in thickened surfaces. In this paper, we study the concordance properties of these invariants. For example, if $K \subset \Sigma \times I$ is ${\mathbb Z}/2$ null-homologous …

ca (code pays fourni par la source)

Toric multisections and curves in rational surfaces

Gabriel Islambouli, Homayun Karimi, Peter Lambert‐Cole, Jeffrey Meier

Pants distances of knotted surfaces in 4-manifolds

Román Aranda, Sarah E. Blackwell, Devashi Gulati, Homayun Karimi et autres

We define a pants distance for knotted surfaces in 4-manifolds, which generalizes the complexity studied by Blair-Campisi-Taylor-Tomova for surfaces in the 4-sphere. We determine that if the distance computed on a given diagram does not surpass a theoretical bound in terms of …

Adequate links in thickened surfaces and the generalized Tait conjectures

Hans U. Boden, Homayun Karimi, Adam S. Sikora

We apply Kauffman bracket skein algebras to develop a theory of skein adequate links in thickened surfaces.We show that any alternating link diagram on a surface is skein adequate.We apply our theory to establish the first and second Tait conjectures for adequate …

ca, us (code pays fourni par la source)

Mock Seifert matrices and unoriented algebraic concordance

Hans U. Boden, Homayun Karimi

A mock Seifert matrix is an integral square matrix representing the Gordon-Litherland form of a pair $(K,F)$, where $K$ is a knot in a thickened surface and $F$ is an unoriented spanning surface for $K$. Using these matrices, we introduce a new …

On knots that divide ribbon knotted surfaces

Hans U. Boden, Ceyhun Elmacioglu, Anshul Guha, Homayun Karimi et autres

We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a knot K, the minimum genus of a ribbon …

A characterization of alternating links in thickened surfaces – CORRIGENDUM

Hans U. Boden, Homayun Karimi

ca (code pays fourni par la source)

The Gordon–Litherland pairing for links in thickened surfaces

Hans U. Boden, Micah Chrisman, Homayun Karimi

We extend the Gordon–Litherland pairing to links in thickened surfaces, and use it to define signature, determinant and nullity invariants for links that bound (unoriented) spanning surfaces. The invariants are seen to depend only on the [Formula: see text]-equivalence class of the …

ca, us (code pays fourni par la source)

The Jones–Krushkal polynomial and minimal diagrams of surface links

Hans U. Boden, Homayun Karimi

We prove a Kauffman–Murasugi–Thistlethwaite theorem for alternating links in thickened surfaces. It implies that any reduced alternating diagram of a link in a thickened surface has minimal crossing number, and any two reduced alternating diagrams of the same link have the same …

fr, ca (code pays fourni par la source)

Toric multisections and curves in rational surfaces

Gabriel Islambouli, Homayun Karimi, Peter Lambert‐Cole, Jeffery L. Meier

We study multisections of embedded surfaces in 4-manifolds admitting effective torus actions. We show that a simply-connected 4-manifold admits a genus one multisection if and only if it admits an effective torus action. Orlik and Raymond showed that these 4-manifolds are precisely …

Classical results for alternating virtual links

Hans U. Boden, Homayun Karimi

We extend some classical results of Bankwitz, Crowell, and Murasugi to the setting of virtual links. For instance, we show that an alternating virtual link is split if and only if it is visibly split, and that the Alexander polynomial of any …