I would like to ask two (related) things about the torus:
The torus can be described as the cartesian product $S^1 \times S^1$ of two circles in $\mathbb{R}^3$. Then one can talk about meridional circles and longitudinal circles. I was wondering - is there a common way to associate the two factors with meridional and longitudinal circles ? That is, is for example the first factor in $S^1 \times S^1$ always used as the longitudinal one ?
Also, I am wondering if I identify two tori along the circle $S^1 \times \{x_0 \}$ - would such an identification be the same as the one obtained by an identification of $\{x_0 \} \times S^1 $ ? This question is related to the first one in that it asks whether there is any kind of natural way to order the product, I guess.
Many thanks for your help!