Consider a polynomialfunction f : C-n --> C with generic fiber F. Let B-f be the bifurcation set of f; hence f induces a smooth locally trivial fibration over C B-f. Then, for any integer q greater than or equal to 0 and any coefficient ring R, there is an associated monodromy representation rho (f)(q) : pi1(C B-f, pt) --> Aut ((H) over tilde (q)(F, R)) in (reduced) homology. Going around a circle in C large enough to contain all of the bifurcation set gives rise to the monodromy operators at infinity, which we denote by M-infinity (f)(q). We show that these monodromy operators at infinity and a certain natural direct sum decomposition of the homology of F in terms of vanishing cycles determine the monodromy representation. The role played by this decomposition is crucial since there are examples of polynomials C-2 --> C having distinct complex monodromy representations but whose monodromy operators at infinity have the same Jordan normal form. [References: 20]
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