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Extensions of umbral calculus. II: Double delta operators, Leibniz extensions and Hattori-Stong theorems. (English) Zbl 0962.05012
Summary: “We continue our programme of extending the Roman-Rota umbral calculus to the setting of delta operators over a graded ring \(E_{*}\) with a view to applications in algebraic topology and the theory of formal group laws. We concentrate on the situation where \(E_{*}\) is free of additive torsion, in which context the central issues are number-theoretic questions of divisibility. We study polynomial algebras which admit the action of two delta operators linked by an invertible power series, and make related constructions motivated by the Hattori-Stong theorem of algebraic topology. Our treatment is couched purely in terms of the umbral calculus, but inspires novel topological applications. In particular we obtain a generalised form of the Hattori-Stong theorem.”
For Part I see N. Ray [Adv. Math. 61, 49-100 (1986; Zbl 0631.05002)].
Reviewer: Reviewer (Berlin)

MSC:
05A40 Umbral calculus
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
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