結び目と多様体の幾何学
メンバー： 合田洋、畠中英里
分野： 数学
所属： 工学研究院
キーワード： 結び目、絡み目、3次元多様体、曲面結び目
ウェブサイト：
研究概要
1次元多様体は線やひもを、2次元多様体は曲面を、3次元多様体はゆがんだ空間を意味します。
我々の研究室では、図形をまげたりのばしたりすることも許容する位相幾何学の立場で幾何学の研究をしています。特に、微分積分、線形代数などを応用して(1)3次元多様体、(2)結び目絡み目、(3)曲面結び目 の研究をしています。
主要論文・参考事項
(1) E. Hatakenaka, T. Satoh,
On the graded quotients of the rings of Fricke characters of free groups,
J. Algebra 430 (2015), 94-118.
(2) H. Goda, H. Matsuda, A. Pajitnov,
Morse-Novikov theory, Heegaard splittings, and closed orbits of gradient flows,
St. Petersburg Math. J. 26 (2015), no. 3, 441-461.
(3) H. Goda, T. Sakasai,
Homology cylinders and sutured manifolds for homologically fibered knots,
Tokyo J. Math. 36 (2013), no. 1, 85-111.
(4) E. Hatakenaka, T. Nosaka,
Some topological aspects of 4-fold symmetric quandle invariants of 3-manifolds,
Internat. J. Math. 23 (2012), no. 7, 1250064, 31 pp.
(5) E. Hatakenaka, Invariants of 3-manifolds derived from covering presentations,
Math. Proc. Cambridge Philos. Soc. 149 (2010), no. 2, 263-295.
お問い合わせ先
東京農工大学・先端産学連携研究推進センター
urac[at]ml.tuat.ac.jp（[at]を@に変換してください）
Geometry of knots and manifolds
Research members： Dr. Hiroshi Goda, Dr. Eri Hatakenaka
Research fields： Mathematics
Departments： Institute of Engeneering
Keywords： knot, link, 3-dimensional manifold, surface knot
Web site：
Summary
1 dimensional manifolds are lines or strings,
2 dimensional ones are surfaces, and
3 dimensional ones mean a curved spaces.
In our laboratories, we study the geometry of manifolds
from the viewpoint of topology, which is the
study of geometrical properties, spatial relations
and invariants.
In particular, we investigate knots & links, surface knots,
and 3-dimensional manifolds
using differential and integral calculus,
linear algebra and so on.
Reference articles and patents
(1) E. Hatakenaka, T. Satoh,
On the graded quotients of the rings of Fricke characters of free groups,
J. Algebra 430 (2015), 94-118.
(2) H. Goda, H. Matsuda, A. Pajitnov,
Morse-Novikov theory, Heegaard splittings, and closed orbits of gradient flows,
St. Petersburg Math. J. 26 (2015), no. 3, 441-461.
(3) H. Goda, T. Sakasai,
Homology cylinders and sutured manifolds for homologically fibered knots,
Tokyo J. Math. 36 (2013), no. 1, 85-111.
(4) E. Hatakenaka, T. Nosaka,
Some topological aspects of 4-fold symmetric quandle invariants of 3-manifolds,
Internat. J. Math. 23 (2012), no. 7, 1250064, 31 pp.
(5) E. Hatakenaka, Invariants of 3-manifolds derived from covering presentations,
Math. Proc. Cambridge Philos. Soc. 149 (2010), no. 2, 263-295.
Contact
University Research Administration Center(URAC),
Tokyo University of Agriculture andTechnology
urac[at]ml.tuat.ac.jp
(Please replace [at] with @.)