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Contemporary Mathematics A topological calculus for formal power series

We propose geometric models for performing computations with formal power series over a commutative ring, including reciprocation, substitution, reversion, and Lagrange inversion. The models are based on a family of complex Bott-Samelson varieties which may be realized as manifolds of flags satisfying appropriate restrictions. We discuss the relationship of the geometric computations with multiple complex cobordism theory, focussing on the dual of the Landweber-Novikov algebra and raising delicate issues concerning the construction of explicit cobordisms. We outline extensions of the calculus to Hurwitz series, appealing to the Faà di Bruno algebra of algebraic combinatorics.