| Academic Year |
2026Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA36000 |
Subject Classification |
Specialized Education |
| Subject Name |
多様幾何特論Ｄ |
Subject Name
（Katakana） |
タヨウキカトクロンデー |
Subject Name in
English |
Topics in Geometry D |
| Instructor |
MURAO TOMO |
Instructor
(Katakana) |
ムラオ トモ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Tues3-4,Fri3-4：SCI E208 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| Lecture using blackboard |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
J
:
Japanese |
| Course Level |
5
:
Graduate Basic
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Knot, Quandle, Quandle coloring, Quandle cocycle invariant, Quandle twisted Alexander invariant |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
This course provides an introduction to knot theory. Knot theory is a branch of low-dimensional topology that studies the ambient isotopy classes of circles embedded in the three-dimensional sphere or three-dimensional Euclidean space. This course introduces various knot invariants defined using an algebraic structure called a quandle. |
| Class Schedule |
lesson1:Knots and links
lesson2:Orientations and mirror images of links
lesson3:Quandles
lesson4:Quandle colorings
lesson5:Free quandles
lesson6:Presentations of quandles
lesson7:Associated groups of quandles
lesson8:Knot quandles
lesson9:Shadow quandle colorings
lesson10:Quandle homology
lesson11:Shadow quandle cocycle invariants
lesson12:Quandle extensions and Alexander pairs
lesson13:Quandle twisted Alexander invariants
lesson14:Column relation matrices and row relation matrices
lesson15:Normalization of Quandle twisted Alexander invariants |
Text/Reference
Books,etc. |
No textbook.
Reference books:「Surface-Knots in 4-Space: An Introduction」, Seiichi Kamada, Springer, 2017 |
PC or AV used in
Class,etc. |
|
| (More Details) |
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
You need to review the contents after each lecture. |
| Requirements |
|
| Grading Method |
Evaluation will be based on homework assignments. |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |