We extend several classical invariants of links in the 3-sphere to links in so-called quasi-cylinders. These invariants include the linking number, the Seifert form, the Alexander module, the Alexander-Conway polynomial and the Murasugi-Tristram-Levine signatures.
"A generalization of several classical invariants of links." Osaka J. Math. 44 (3) 531 - 561, September 2007.