Fall 2021 Combinatorial Topology (MAS 430. 25.430)
Time: Monday, Wednesday 1:00-2:15
Lecture room: 3434
Instructor: Suhyoung Choi 4403(office)
Office Hours:
schoi at math dot kaist dot ac dot kr Phone: 2732
Prerequisite: MAS 331 Topology
Course book: Topology, J. Munkres (secondary: A basic course in Algebraic topology, W.S. Massey)
Topics: Fundamental groups, Surface theory, Covering space theory
Lectures are given by vidoes. Zoom presentation meetings will be scheduled one or two weeks ahead.
Grading: Final (150 pts.) Midterm (150 pts.) Homework (100 pts.) Class contribution (25 pts.) Attendance
(25 pts.) Total 450pts
There will be Zoom presentations of your homework solutions. These are 50% of the homework grades. The midterm and the final will be take-home exams. You can cowork for homework. However, you cannot help one another at all for take-home exams. There will be peer grading which will be counted for class contributions.
Zoom session links will beprovided in the KLMS.
Course schedules:
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Week
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Date
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Lecture
plan
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|
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1
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Aug. 30, Sept. 1
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Introduction, S. 51; S. 52, Fundamental groups
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|
|
2
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Sept. 6, 8
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S.53, S.54, Covering spaces
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|
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3
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Sept.13, 15
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S. 55, S.56, S.57, Retractions and fixed points
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|
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4
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Sept.
20, 22
|
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No classes (National Holidays, Chuseok) |
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5
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Sept. 27, 29
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S. 58; S. 59, S. 60, Homotopy types
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|
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6.
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Oct. (4), 6
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S. 61, S.62; S. 63, Separation theorems
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Oct. 4th may be a holiday
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|
7
|
Oct.
(11), 13
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S. 64, S. 65, S. 66, Winding numbers
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Oct. 11th may be a holiday
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8
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Oct. 18, 20
|
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Midterm period
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9
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Oct.
25, 27
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S. 67, S. 68, S. 69, Seifert van-Kampen theorem
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|
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10
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Nov. 1, 3
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S. 70, S. 71; S. 72, S.73 Seifert van-Kampen theorem
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11
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Nov. 8, 10
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S. 74, S. 75; S. 76, Classification of surfaces
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|
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12
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Nov. 15, 17
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S. 77, S. 78, Classification of surfaces
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|
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13
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Nov. 22, 24
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S. 79, S. 80, Classification of covering spaces
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|
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14
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Nov. 29, (Dec 1)
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S. 81; S. 82, Classification of covering spaces
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(Dec. 1st is the KAIST entrance exam day)
|
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15
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Dec 6, 8
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S. 83; S. 84, S. 85, Application to graph theory
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|
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16
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Dec. 13, 15
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Final
exam period
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