# An Introduction to Low Dimensional Topology (MATH577) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
An Introduction to Low Dimensional Topology MATH577 Area Elective 3 0 0 3 5
Pre-requisite Course(s)
Consent of the Department
Course Language English Elective Courses Ph.D. Face To Face Discussion, Question and Answer. The aim of this course is to introduce the basic techniques to work with manifolds in low dimensions. To approach this main goal, the knot theory and surfaces, which touches upon many branches of mathematics, will be introduced. Elementary linear algebra and some group theory which are taught in the undergraduate program are sufficient as a background. The students who succeeded in this course; learn knots, links and their invariants understand how knots and links are related to the two and three dimensional manifolds learn the braids, their relations to knots and links and Seifert surfaces also to mapping class groups learn the fundamental tools of three manifolds such as Heegaard decompositions, surgery, branched coverings etc. Knots, links and their invariants, Seifert surfaces, braids, mapping class groups, Heegaard decompositions, lens spaces and surface homeomorphisms, surgery of 3-manifolds, branched coverings.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Knots, Links and Ribbons pp. 1-22
2 Knot and Link Invariants pp. 23-46
3 Seifert Matrices and Surfaces pp. 118-144, pp.200-232 (D.Rolfsen)
4 Braids pp. 47-66
5 3-Manifolds pp.67-72
6 Heegaard Decompositions of 3- Manifolds pp. 73-76
7 Midterm
8 Lens Spaces pp. 77-82
9 Homeomorphisms of Surfaces pp.83-89
10 Mapping Class Groups pp. 90-94
11 Fibred Knots and Links Open Book Decompositions pp.323-341 (D.Rolfsen)
12 Surgery on 3-Manifolds pp. 95-107
13 Surgery on 3-Manifolds (Continue) pp. 108-126
14 Branched Coverings pp. 127-151
15 Review
16 Final Exam

### Sources

Course Book 1. and 3-Manifolds: An Introductions to the New Invariants in Low-Dimensional Topology, Prasolov, Sossinsky, 1996, AMS.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 3 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 5 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team
2 Ability to evaluate research topics and comment with scientific reasoning
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level
7 Contribute scientific and technological advancements on engineering domain of his/her interest area
8 Contribute industrial and scientific advancements to improve the society through research activities

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class
Presentation/Seminar Prepration
Project
Report
Homework Assignments 3 5 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 10 10
Prepration of Final Exams/Final Jury 1 10 10