The disentanglement of an analytic map germ \(f:( \mathbb{C}^n,0)\to (\mathbb{C}^p,0)\) is a topological object replacing the more common Milnor filter of a function germ \(g:(\mathbb{C}^n,0) \to(\mathbb{C},0)\).
By analogy with classical results in Milnor fibers, the author establishes bouquet and join theorems for such disentanglements. Though the final results are quite similar to the Milnor fiter case, the proofs are completely different and substantially more difficult.