J. Knot Theory Ramifications 27(1843011, 33 pp) 1843011-1843011 2018年 [査読有り]
In this paper, we introduce the (co)homology group of a multiple conjugation biquandle. It is the (co)homology group of the prismatic chain complex, which is related to the homology of foams introduced by J. S. Carter, modulo a certain subchain co...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 26(12) 2017年10月 [査読有り]
We introduce an up-down coloring of a virtual-link (or classical-link) diagram. The colorabilities give a lower bound of the minimum number of Reidemeister moves of type II which are needed between two 2-component virtual-link (or classical-link) ...
Algebraic and Geometric Topology 16(4) 2443-2458 2016年 [査読有り]
The Roseman moves are seven types of local modifications for surface-link diagrams in 3-space which generate ambient isotopies of surface-links in 4-space. In this paper, we focus on Roseman moves involving triple points, one of which is the famou...
TOPOLOGY AND ITS APPLICATIONS 196 921-930 2015年12月 [査読有り]
Racks do not give us invariants of surface-knots in general. For example, if a surface-knot diagram has branch points (and a rack which we use satisfies some mild condition), then it admits no rack colorings. In this paper, we investigate rack col...
上智大学
理工学部