Title: The infinite Fibonacci groups and relative asphericity,
Abstract: We prove that the generalised Fibonacci group F(r,n) is infinite for (r,n) in
{(7 + 5k,5), (8 + 5k,5)} where k is greater than or equal to 0. This together
with previously known results yields a complete classification of the finite
F(r,n), a problem that has its origins in a question by J H Conway in 1965. The
method is to show that a related relative presentation is aspherical from which
it can be deduced that the groups are infinite.