that corresponds to the complement of a trivial (but essencial) torus knot in a open solid torus. For those -Fico had mention- they are called cable spaces and have nice foliation into circles. Its name is CS(1,0). Can you see what is CS(2,1)?
Edit at: utc-6 = 11:50 approx
you could also say the trivial I-bundle over the torus
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