I got it! This is awesome.
I got \alpha(t)=m(1-t) which gave the well defined homotopy
H(s,t) = \begin{cases} e^{2\pi i (m+n) st}e^{2\pi i m 2 s (1-t)} & \textrm{for }s \in [0,1/2] \\
e^{2\pi i(m+n)st}e^{2\pi i n 2 (2s-1)(1-t)}e^{2\pi i m(1-t)} & \textrm{for }s \in [1/2,1]
\end{cases}...
Thank you for the help.
So far what I have is for s in [0, 1/2]
H(s,t)= e^{2\pi i(m+n)st}e^{2\pi im2s(1-t))}
and for s in [1/2, 1], I have:
H(s,t)= e^{2\pi i(m+n)st}e^{2\pi in(2s-1)(1-t))}
This satisfies our conditions for a homotopy for t=0 and for t=1.
Unfortunately, when we consider s...
Hi,
I am reading J.P. May's book on "A Concise Course in Algebraic Topology" and have approached the calculation where \pi_{1}(S^{1})\congZ
He defines a loop f_{n} by e^{2\pi ins}
I want to show that [f_{n}][f_{m}]=[f_{m+n}]
I understand this as trying to find a homotopy between...