Shin SATOH

Shin SATOH

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

Research Field : Diagrammatic Surface-Knot Theory
Research Summary : A surface-knot is a possibly non-orientable closed surface embedded in Euclidian 4-space. Though it is analogous to a 1-dimensional knot in 3-space, it has many different properties from 1- or higher-dimensional knots. We visualize a surface-knot by slicing it with parallel hyperplanes like CT scan or by taking a projection into 3-space to obtain a shadow of the surface-knot. The goal of my study is to handle and deform a surface-knot in 4-space without restraint. I am interested in the triple point number, virtual and welded knot presentation, surface-knot quandle, colorability, and so on.
Primary Publications :
  1. S. Satoh: Virtual knot presentations of ribbon torus-knots, J. Knot Theory Ramifications 9 (2000) 531-542.
  2. S. Satoh: Triple point invariants of non-orientable surface-links, Tolology Appl. 121 (2002) 207-218.
  3. S. Satoh and A. Shima: The 2-twist-spun trefoil has the triple point number four, Trans. Amer. Math. Soc. 356 (2004) 1007--1024.
  4. T. Kishino and S. Satoh: A note on non-classical virtual knots, J. Knot Theory Ramifications 13 (2004) 845--856.
  5. M. Saito and S. Satoh: The spun trefoil needs four broken sheets, J. Knot Theory Ramifications 14 (2005) 853-858.
  6. T. Nakamura, Y. Nakanishi, and S. Satoh, The pallet graph of a Fox coloring, Yokohama Math. J. 59 (2013), 91-97.
  7. S. Satoh and K. Taniguchi, The writhes of a virtual knot, Fund. Math. 225 (2014), 327-342.
  8. 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.
  9. T. Nakamura, Y. Nakanishi, and S. Satoh, On effective 9-colorings for knots, J. Knot Theory Ramifications 23 (2014), no. 12, 1450059, 15pp.