Topology and geometry of the general composition of formal power series -- towards Fréchet-Lie group-like formalism

2024/09/15 by Dawid Bugajewski, Bugajewski, Dawid · 1 citation
Mathematics · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2409.09853

Abstract

In this article, we study the properties of the autonomous superposition operator on the space of formal power series, including those with nonzero constant term. We prove its continuity and smoothness with respect to the topology of pointwise convergence and a natural Fréchet manifold structure. A necessary and sufficient condition for the left composition inverse of a formal power series to exist is provided. We also present some properties of the Fréchet-Lie group structures on the set of nonunit formal power series.

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• On Riordan groups involving formal semi-Laurent series and their Lie group structure

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