Algebraic Topology an Introduction

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

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