Shin SATOH 
Shin SATOH
Department of Mathematics,
Graduate School of Science, Kobe University 
Division : Geometry
Professor 
Building B, Room 424

Research Field :
Diagrammatic SurfaceKnot Theory


Research Summary :
A surfaceknot is a possibly nonorientable closed surface embedded in Euclidian 4space. Though it is analogous to a 1dimensional knot in 3space, it has many different properties from 1 or higherdimensional knots. We visualize a surfaceknot by slicing it with parallel hyperplanes like CT scan or by taking a projection into 3space to obtain a shadow of the surfaceknot. The goal of my study is to handle and deform a surfaceknot in 4space without restraint. I am interested in the triple point number, virtual and welded knot presentation, surfaceknot quandle, colorability, and so on.


Primary Publications : 
 S. Satoh: Virtual knot presentations of ribbon torusknots, J. Knot Theory Ramifications 9 (2000) 531542.
 S. Satoh: Triple point invariants of nonorientable surfacelinks, Tolology Appl. 121 (2002) 207218.
 S. Satoh and A. Shima: The 2twistspun trefoil has the triple point number four, Trans. Amer. Math. Soc. 356 (2004) 10071024.
 T. Kishino and S. Satoh: A note on nonclassical virtual knots, J. Knot Theory Ramifications 13 (2004) 845856.
 M. Saito and S. Satoh: The spun trefoil needs four broken sheets, J. Knot Theory Ramifications 14 (2005) 853858.
 T. Nakamura, Y. Nakanishi, and S. Satoh, The pallet graph of a Fox coloring, Yokohama Math. J. 59 (2013), 9197.
 S. Satoh and K. Taniguchi, The writhes of a virtual knot, Fund. Math. 225 (2014), 327342.
 T. Nakamura, Y. Nakanishi, S. Satoh, and Y. Tomiyama, The state numbers of a virtual knot, J. Knot Theory Ramifications 23 (2014), no. 3, 1450016, 27 pp.
 T. Nakamura, Y. Nakanishi, and S. Satoh, On effective 9colorings for knots, J. Knot Theory Ramifications 23 (2014), no. 12, 1450059, 15pp.


