Math 4432(Algebraic) TopologySpring 2015 
J.J. van Wijk & A. Cohen 


Week  Date  Topics  Reading  Homework  Notes 
1  Jan 5  Overview  Autobiography  
Jan 7  Topological equivalence  1.4  
Jan 9  Topological equivalence  1.4  1.4 # 8, 9, 10, 12, 15  Last day to drop w/o W  
2  Jan 12  Topological invariants  1.5  
Jan 14  Topological invariants  1.5  1.5 # 7, 10, 12, 13  
Jan 16  Isotopy  1.6  1.6 # 4, 5, 7, 9  
3  Jan 19  MLK Day  
Jan 21  Knots  2.1  2.1 # 7, 9b, 10  
Jan 23  Knot diagrams  2.2  2.2 # 11, 12, 14, 15  
4  Jan 26  Reidemeister moves  2.3  2.3 # 3, 10, 11  
Jan 28  Colorings  2.4  2.4 # 1, 5  
Jan 30  First Midterm  1.41.6, 2.12.4  Solutions  
5  Feb 2  Alexander polynomial  2.5  2.4 # 8  
Feb 4  Alexander polynomial  2.5  2.5 # 1,3,14,16  
Feb 6  Skein relations  2.6  2.6 # 6,7,9,11  
6  Feb 9  Jones polynomial  2.7  2.7 # 3,10,11  
Feb 11  Surfaces  3.1  3.1 # 2, 3, 7, 10  
Feb 13  Cutting and pasting  3.2  3.2 # 1, 4, 6, 8  
7  Feb 16  Euler characteristic  3.3  3.3 # 1, 4  
Feb 18  Classification of surfaces  3.4  3.4 # 3, 4, 11  
Feb 20  Seifert surfaces  3.5  3.5 # 1, 2  
8  Feb 23  Mapping class groups  OHGGT  Read / make comments  
Feb 25  Snow day  
Feb 27  Mapping class groups  OHGGT  Read / make comments  Last day to drop with W Last day to elect P/F 

9  Mar 2  3manifolds  4.1  4.1 # 5, 7, 8  
Mar 4  Euler characteristic  4.2  4.2 # 3, 4, 5, 6, 9  
Mar 6  Second Midterm  2.52.7, 3.13.5  
Mar 9  Gluing polyhedra  4.3  4.3 # 2, 5, 6, 9  
Mar 11  Heegaard splittings  4.4  4.4 # 7  
Mar 13  Heegaard splittings  4.4  4.4 # 11  
Mar 16  Spring break  
11  Mar 23  Fixed points in intervals Sharkovsky's theorem 
5.1  5.1 # 8, 9, 10  
Mar 25  Contraction mapping theorem  5.2  5.2 # 2, 3, 7  
Mar 27  Sperner's lemma  5.3  5.3 # 2  
12  Mar 30  Brouwer FPT  5.4  5.4 # Prove Ham Sandwich Thm  
Apr 1  Fundamental group  6.1  6.1 # 5  
Apr 3  Fundamental group  6.1  6.1 # 6  
13  Apr 6  Algebraic properties  6.2  6.2 # 2  
Apr 8  Invariance  6.3  6.3 # 3, 6, 8  
Apr 10  Third Midterm  4.14.4, 5.15.4  
14  Apr 13  Spheres  6.4  6.4 # 9, 10, 11, 12, 13, 15, 18  
Apr 15  Words and relations  6.5  6.5 # 5, 7, 10  
Apr 17  Words and relations  6.5  6.5 # 14  
15  Apr 20  Covering spaces  6.5  
Apr 22  Covering spaces  6.5  
Apr 24  Quintics  Notes  
16  Apr 29  Final Exam  1.41.6, 2.12.7, 3.13.5, 4.14.4, 5.15.4, 6.16.6 
The topological proof of AbelRuffini theorem, Henryk Zoladek
The Sharkovsky Theorem: A Natural Direct Proof, Keith Burns and Boris Hasselblatt
The Knot Book, Colin Adams
Teruaki, Kazushi Ahara
Topology, James Munkres
The Shape of Space, Jeffrey Weeks
Understanding Topology and Shapefiles, David M. Theobald www.math.psu.edu/tabachni/Books/taba.pdf