If h is a path in X starting at x0 and ending at x1 then we

have deﬁned an isomorphism βh : π1 (X, x1 ) → π1 (X, x0 ).

Now suppose that x0 = x1 .

In that case βh : π1 (X, x0 ) → π1 (X, x0 ).

In other words βh is an automorphism of π1 (X, x0 ). Can you describe this

automorphism more concretely?