國立中央大學一百零五學年度上學期代數拓樸課程網頁
宣佈事項：
[更正]因放颱風假，教師節星期三(9/28)不上課。
作業：
作業一 (due 10/5)：p18 #2, p19 #10, #17(b)
作業二 (due 10/12) : p19 #19, p38 #3
作業三 (due 10/19) : p39 #16(a)(b)(d)(f)
作業四 (due 10/26) : p53 #4, #7, #8
作業五 (due 11/2) : p79 #2, #9
作業六 (due 11/30) : p131 #1, #4, #5
作業七 (due 12/7) : p132 #11, #12, #14(第一個問題)
作業八 (due 12/14) : p132 #15, #16(a)(b)
作業九 (due 12/21) : p133 #27(a), p155 #2(前兩個問題), #3(第一個問題)
作業十 (due 12/28) : p155 #6, p156 #10
課程進度 :
Week1:
9/14: Review on point-set topology 講義
Week2:
9/21 : Chapter 0. Some underlying geometric notions
Homotopy and homotopy type 講義,
Cell complexes 講義
Week3:
9/28: National holiday, No class
Week4:
10/5: Operations on spaces 講義
Chapter 1. The fundamental group
1.1. Basic constructions
Paths and homotopy 講義
Week5:
10/12: The fundamental group of the circle 講義
Induced homomorphisms 講義
Week6:
10/19: 1.2. Van Kampen's Theorem
The Van Kampen's Theorem 講義
Applications to Cell Complexes 講義
Week7:
10/26: 1.3 Covering spaces
Lifting properties 講義
Week8:
11/2: The classification of covering spaces 講義
Week9:
11/9: 期中考(口頭報告)
Week10:
11/16: 運動會
Week11:
11/23: Chapter 2. Homology
2.1 Simplicial and Singular Homology
Delta-complexes 講義
Simplicial Homology 講義
Week12:
11/30: Singular Homology 講義
Homotopy Invariance 講義
Exact Sequences 講義
Week13:
12/7: Exact Sequences(continued) 講義
Relative Homology Groups 講義
Week14:
12/14: Excision 講義
Chapter 2. Homology
2.2 Computations and Applications
Degree 講義
Week15:
12/21: Computation of degrees 講義
Cellular Homology 講義
Week16:
12/28: Cellular Homology(continued) 講義
Euler Characteristic 講義
Mayer-Vietoris sequences 講義
Week17:
1/4: Reidemeister torsion 講義
Week18:
1/11: 期末考(口頭報告)
Office hour and Office:
星期二下午1點至3點, 鴻經館418, 分機：65152
課本：Algebraic Topology, Allen Hatcher, Link
評量配分比重：
作業50%+期中考20%+期末考20%+出席率10%
授課大綱：
The fundamental group:
1. Basic constructions
2. Van Kampen’s theorem
3. Covering spaces
Homology:
1. Cell complexes, simplicial and singular homology
2. Computations and applications
3. The formal viewpoint
If time permits, we will also learn
Cohomology:
1. Cohomology groups
2. Cup product
3. Poincare duality