| Academic Year |
2025Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA34000 |
Subject Classification |
Specialized Education |
| Subject Name |
多様幾何特論Ｂ |
Subject Name
（Katakana） |
タヨウキカトクロンビー |
Subject Name in
English |
Topics in Geometry B |
| Instructor |
To be announced.,FUJIMORI SHOICHI |
Instructor
(Katakana) |
タントウキョウインミテイ,フジモリ ショウイチ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Weds3-4,Fri5-6：Online |
| 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, Knot group, Alexander polynomial |
| 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.
In this course, we first cover the fundamentals of knot theory and then focus on the classical knot invariant known as the Alexander polynomial.
|
| Class Schedule |
lesson1:Knots and links
lesson2:Various knots
lesson3:Orientations of links and linking numbers
lesson4:Category and functor
lesson5:Free groups
lesson6:Presentations of groups
lesson7:Tietze transformations
lesson8:Knot groups
lesson9:Paths and homotopy
lesson10:Fundamental groups
lesson11:Elementary ideals
lesson12:Abelianizations of groups
lesson13:Fox derivatives
lesson14:Alexander polynomials
lesson15:Calculations of Alexander polynomials |
Text/Reference
Books,etc. |
No textbook.
Reference books:「Introduction to Knot Theory」, R. H. Crowell, R. H. Fox., Springer New York, 1963, ISBN:1461299373 |
PC or AV used in
Class,etc. |
|
| (More Details) |
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| 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. |