4 citations · 9 across the 9 of their papers we have counts for
10 papers
Remark on twists of Frobenius algebra and link homology
Noboru Ito, Keita Nakagane, Jun Yoshida
We discuss twists on Frobenius algebras in the context of link homology. In his paper in 2006, Khovanov asserted that a twist of a Frobenius algebra yields an isomorphic chain comp…
On the four-term relation on Khovanov homology
Noboru Ito, Jun Yoshida
The goal of this paper is to prove a categorified analogue of Kontsevich's relation on Vassiliev derivatives of Khovanov homology.
Decomposition of the first Vassiliev derivative of Khovanov homology and its application
Jun Yoshida
Khovanov homology extends to singular links via a categorified analogue of Vassiliev skein relation. In view of Vassiliev theory, the extended Khovanov homology can be seen as Vass…
A cobordism realizing crossing change on tangle homology and a categorified Vassiliev skein relation
Noboru Ito, Jun Yoshida
In this paper, we discuss degree 0 crossing change on Khovanov homology in terms of cobordisms. Namely, using Bar-Natan's formalism of Khovanov homology, we introduce a sum of cobo…
Crossing change on Khovanov homology and a categorified Vassiliev skein relation
Noboru Ito, Jun Yoshida
Khovanov homology is a categorification of the Jones polynomial, so it may be seen as a kind of quantum invariant of knots and links. Although polynomial quantum invariants are dee…
Categories of operators and actions of group operads
Jun Yoshida
We propose a new model for multicategories with symmetries with respect to Zhang's group operads. The fully faithful embedding of the category of group operads into that of crossed…
Group operads as crossed interval groups
Jun Yoshida
The goal of the paper is to establish and to investigate a fully faithful embedding of the category of group operads into that of crossed interval groups. For this, we introduce a…
Limits and colimits of crossed groups
Jun Yoshida
Although the notion of crossed groups was originally introduced only in the simplicial case, the definition makes sense in the other categories. For instance, Batanin and Markl stu…
Transversality theorem in highly relative situations and its application
Jun Yoshida
In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relatin…
A general method to construct cube-like categories and applications to homotopy theory
Jun Yoshida
In this paper, we introduce a method to construct new categories which look like "cubes", and discuss model structures on the presheaf categories over them. First, we introduce a n…