KAMADA, Seiichi

Email kamada(
Keywords Low dimensional topology, Knot theory

My research area is topology (geometric topology-- knot theory, low dimensional topology). I have been working on surface-links in 4-space, including 2-knots and 2-links, 2-dimensional braids, braided surfaces, and 4-manifolds.

Surface-links are closed surfaces smoothly embedded in the 4-space, and they are considered equivalent if they are ambiently isotopic. It is a quite difficult problem to decide whether two given surface-links are equivalent or not. Invariants are often used to show that two surface-links are not equivalent. However, few invariants are known for surface-links. I am interested in studying surface-links and their invariants using "quandles" and graphics so-called "charts".

A quandle is an algebra with a binary operation which satisfies three axioms corresponding to Reidemeister moves in knot theory. A homology theory of quandles was established and we can use it for construction of invariants for surface-links. 2-dimensional braids, or surface braids, are a generalization of classical braids. They are in one-to-one correspondence to oriented surface-links in 4-space modulo certain basics moves. As a method of describing 2-dimensional braids, a chart description was introduced. This method has been extended in a general theory of charts. For example, charts can be used for studies of Lefschets fibrations of 4-manifolds.