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The workshop “Quandles and Symmetric Spaces” has been held annually since 2018. This volume records the abstracts and the slides of talks presented in this workshop on 2024.

The workshop “Quandles and Symmetric Spaces” has been held annually since 2018. This volume records the abstracts and the slides of talks presented in this workshop on 2024.

This international academic symposium focuses on recent progress in mathematical visualization, and will promote discussions between researchers in this field from abroad and in Japan, aiming to encourage future collaborations.

The workshop "Quandles and symmetric spaces" has been held annually since 2018. This volume records the abstracts and some slides of talks presented in this workshop on 2019 and 2020.

The workshop "Quandles and Symmetric Spaces" has been held annually since 2018. This volume records the abstracts and the slides of talks presented in this workshop on 2021.

The workshop "Quandles and symmetric spaces" has been held annually since 2018. This volume records the abstracts and some slides of talks presented in this workshop on 2019 and 2020.

The workshop "Quandles and Symmetric Spaces" has been held annually since 2018. This volume records the abstracts and the slides of talks presented in this workshop on 2021.

The workshop "Quandles and Symmetric Spaces" has been held annually since 2018. This volume records the abstracts and the slides of talks presented in this workshop on 2021.

We present an algorithm that takes as input any element B of the loop braid group and constructs a polynomial f : R-5 -> R-2 such that the intersection of the vanishing set of f and the unit 4-sphere contains the closure of B. The polynomials can be used to create real analytic timedependent vector fields with zero divergence and closed flow lines that move as prescribed by B. We also show how a family of surface braids in C x S-1 x S-1 without branch points can be constructed as the vanishing set of a holomorphic polynomial f : C-3 -> C on C x S-1 x S-1 subset of C-3. Both constructions allow us to give upper bounds on the degree of the polynomials.

This international academic symposium focuses on recent progress in mathematical visualization, and will promote discussions between researchers in this field from abroad and in Japan, aiming to encourage future collaborations.

This international academic symposium focuses on recent progress in mathematical visualization, and will promote discussions between researchers in this field from abroad and in Japan, aiming to encourage future collaborations.

The workshop "Quandles and symmetric spaces" has been held annually since 2018. This volume records the abstracts and some slides of talks presented in this workshop on 2019 and 2020.

Doodles were introduced in [7] but were restricted to embedded circles in the 2-sphere. Khovanov, [15], extended the idea to immersed circles in the 2-sphere. In this paper we further extend the range of doodles to any closed oriented surface….

Doodles were introduced in [7] but were restricted to embedded circles in the 2-sphere. Khovanov, [15], extended the idea to immersed circles in the 2-sphere. In this paper we further extend the range of doodles to any closed oriented surface….

We discuss Gauss codes of virtual diagrams and virtual doodles. The notion of a left canonical Gauss code is introduced and it is shown that oriented virtual doodles are uniquely presented by left canonical Gauss codes.

We discuss Gauss codes of virtual diagrams and virtual doodles. The notion of a left canonical Gauss code is introduced and it is shown that oriented virtual doodles are uniquely presented by left canonical Gauss codes.

Braided surfaces are surfaces embedded or immersed in the bidisk D^2×D^2 which are projected onto the second factor of the bidisk as branched covering maps. A simple and embedded braided surface is described by a graph in the 2-disk, called a chart. We generalize the chart description method so that one can consider braided surfaces which are not necessarily simple or embedded. We show that if a braided surface is regular, then it can be described by a chart called regular, and that such a chart is unique up to regular chart move equivalence.

Twisted links are a generalization of virtual links. As virtual links correspond to abstract links on orientable surfaces, twisted links correspond to abstract links on (possibly non-orientable) surfaces. In this paper, we introduce the notion of the double covering of a twisted link....

Twisted links are a generalization of virtual links. As virtual links correspond to abstract links on orientable surfaces, twisted links correspond to abstract links on (possibly non-orientable) surfaces. In this paper, we introduce the notion of the double covering of a twisted link....

J. Boyle classified 1-handles attached to surface-knots, that are closed and connected surfaces embedded in the Euclidean 4-space, in the case that the surfaces are oriented and 1-handles are orientable with respect to the orientations of the surfaces. In that case, the equivalence classes of 1-handles correspond to the equivalence classes of cords attached to the surface-knot, and correspond to the double cosets of the peripheral subgroup of the knot group....

type:text, Various topological objects; 2-dimensional braids, braided surfaces, Lefschetz fibrations of 4-manifolds, algebraic curves, etc., can be treated by their monodromy representations. We introduce a graphical method, called the chart description method, to describe and calculate such monodromy representations. This method is, in a sense, a generalization of the picture method.

Various topological objects; 2-dimensional braids, braided surfaces, Lefschetz fibrations of 4-manifolds, algebraic curves, etc., can be treated by their monodromy representations. We introduce a graphical method, called the chart description method, to describe and calculate such monodromy representations. This method is, in a sense, a generalization of the picture method.

Various topological objects; 2-dimensional braids, braided surfaces, Lefschetz fibrations of 4-manifolds, algebraic curves, etc., can be treated by their monodromy representations. We introduce a graphical method, called the chart description method, to describe and calculate such monodromy representations. This method is, in a sense, a generalization of the picture method.