• twisted homology
• braids
• tangles
• links
• multivariate Levine-Tristram signature

The focus of this thesis is the study of certain link isotopy invariants, and we mostly concentrate on the multivariate Levine-Tristram signatures. Specifically, we study a generalization of the Gambaudo-Ghys formula, which deals with ordinary Levine-Tristram signatures, to the multivariate case. This result, proven by D. Cimasoni and A. Conway, was obtained with a geometrical approach, interpreting the multivariate signature as the signature of some branched covers of the four-ball. With a different interpretation, which makes use of twisted homology, we manage to extend their result.