MA 651: Topology II

Kate Ponto
Spring 2026

Syllabus

Announcements



Homework



Date Due Pages of the book to read Problems to turn in (from the end of the chapter!)
4/29 159-178 6-2, 6-3, 6-6, Additive invariants
4/22 3 and 4 of Questions for long exact sequences , Question for relative homology and excision
4/15 p 115-126 of Hatcher Questions for homology
Questions for long exact sequences For this one only problems 1 and 2
4/8 360-365
4/1 346-359 13-2, 13-6 (You can use the facts that H_0(B^n)=Z and zero in other degrees, H_p(S^n) is Z if p=0 or n and zero otherwise), 13-7
3/25 Section 1.A, 339-345 10-5, 10-6, Hatcher 1.A.3, 1.A.5. 10-11 (a,b)
3/11 251-273 9-1, 9-2, 10-1, 10-2, 10-9
3/4 315-318, 233-241 12-2, 12-3, 12-4, 12-9, 12-12 (For 12-9 you might want to use that the fundamental group of the Klein bottle is generated by elements a and b subject to the relation bab^{-1}=a^{-1}.)
2/25 307-314 11-18, 11-19, 11-20 (You can have the fact that the identity map of S^2 is not null homotopic.)
2/18 292-302 11-12, 11-13, 11-16, 11-17
2/11 224- 229, 277-291 8-2, 8-6, 8-7, 8-8, 11-4, 11-7, 11-14
1/28 206-208, 217-224 7-6, 7-9, 8-1 (You can assume the fundamental group of the circle is non-trivial and that of a wedge of two circles is non abelian)
1/21 183-205 7-2, 7-3, 7-5, 7-4