HOMEWORK 5 – 2022
Exercise 1. Construct a CW-complex X with the following homology groups:
Hn(X) =



Z, for n = 0;
Z ⊕ Z12, for n = 2022;
Z6, for n = 2023;
0, otherwise.
Exercise 2. Let X and Y be connected CW complexes. Describe reduced cohomology
ring ¯H∗
(X ∨ Y ; Z) in terms of cohomology rings ¯H∗
(X; Z) and ¯H∗
(Y ; Z).
1