#### Algebraic TopologyWilliam Massey

##### Chapter 2

• Exercise 3.1 Determining when two classes of paths from $x$ to $y$ give rise to the sime isomorphism between fundamental groups $\pi(X, x)$ and $\pi(X, y)$
• Exercise 3.2 If any two classes of paths from $x$ to $y$ give rise to the sime isomorphism between fundamental groups $\pi(X, x)$ and $\pi(X, y)$, then the fundamental group is Abelian
• Exercise 4.3 Given a retract $r$ and the inclusion $i$, and their induced homomorphisms $r_*$ and $i_*$, the fundamental group of the space is the direct product of $\im(i_*)$ and $\ker(r_*)$
• Exercise 7.4 Based inclusions into a product space give rise to an isomorphism between the product of the fundamental groups and the fundamental group of the product
• Exercise 7.5 A theorem about paths in a topological group
• Exercise 7.6 A continuation of the previous exercise about topological groups
##### Chapter 3

• Exercise 4.3 A commutative diagram dealing with free products of groups
• Exercise 4.4 Elements of finite order in a free product of groups are either “pure” elements of the components or conjugates of “pure” elements