# Another algebra question in algebraic topology

1. Apr 2, 2009

### quasar987

In the proof of Proposition 3A.5 in Hatcher p.265 (http://www.math.cornell.edu/~hatcher/AT/ATch3.4.pdf), at the bottow of the page, he writes,

"Since the squares commute, there is induced a map Tor(A,B) -->Tor(B,A), [...]"

How does this follow? The map Tor(A,B)-->$A\otimes F_1$ is the connecting homomorphism coming from the long exact sequence (see (6) and its proof) and Tor(B,A)-->$F_1\otimes A$ is inclusion.

It one starts with an element x of Tor(A,B), then pushes it to $A\otimes F_1$ to an element x' and then to $F_1\otimes A$ to an element x'', there is no guarantee as far as I can see that there will be a y in Tor(B,A) with y=x''...

Thanks for any help.

2. Apr 3, 2009

Solved.