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Uspekhi Mat. Nauk, 2013, Volume 68, Issue 1(409), Pages 3–76 (Mi umn9471)  

This article is cited in 8 scientific papers (total in 8 papers)

Algebra, geometry, and topology of the substitution group of formal power series

I. K. Babenkoab

a Université Montpellier II, Montpellier, France
b Moscow State University

Abstract: A systematic description is given of properties of the group $\mathscr{J}(\mathbf{k})$ of formal power series in one variable with coefficients in a commutative unitary ring $\mathbf{k}$. This topological group has been studied intensively over the past 20 years, and a number of interesting results on its structure have been obtained. Here it is indicated how the group $\mathscr{J}(\mathbf{k})$ arises in several different areas of mathematics, such as complex cobordism or symplectic topology. Also considered is how the general structure of the group of complex formal power series is connected with classical problems of local uniformisation and the embedding of the germ of a holomorphic map in a flow.
Bibliography: 115 titles.

Keywords: formal power series, topological group, pro-$p$-group, inverse limit.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00257-a
11-01-90413-Укр-ф-а


DOI: https://doi.org/10.4213/rm9471

Full text: PDF file (1118 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2013, 68:1, 1–68

Bibliographic databases:

Document Type: Article
UDC: 512.54+515.1+517.537.32
MSC: 20E18, 20F22, 22A05, 22A10
Received: 28.02.2012

Citation: I. K. Babenko, “Algebra, geometry, and topology of the substitution group of formal power series”, Uspekhi Mat. Nauk, 68:1(409) (2013), 3–76; Russian Math. Surveys, 68:1 (2013), 1–68

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Buchstaber, “Complex cobordism and formal groups”, Russian Math. Surveys, 67:5 (2012), 891–950  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. I. Babenko, S. Bogatyi, “On topological properties of the formal power series substitution group”, Enseign. Math., 59:3-4 (2013), 271–286  crossref  mathscinet  zmath
    3. J. Mostovoy, J. M. Pérez-Izquierdo, I. P. Shestakov, “Nilpotent Sabinin algebras”, J. Algebra, 419 (2014), 95–123  crossref  mathscinet  zmath  isi  elib  scopus
    4. Ya. V. Abramov, “Artin–Hasse Exponential Mapping, Algebraic Groups in Positive Characteristic, and the Nottingham Group”, Math. Notes, 97:1 (2015), 3–11  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. D. D. Kiselev, “Explicit Embeddings of Finite abelian $p$-Groups in the Group $\mathcal J(\mathbb F_p)$”, Math. Notes, 97:1 (2015), 63–68  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. S. I. Bogataya, S. A. Bogatyi, D. D. Kiselev, “Powers of elements of the series substitution group J(Z(2))”, Topol. and Appl., 201 (2016), 29–56  crossref  mathscinet  zmath  isi  scopus
    7. G.-S. Cheon, A. Luzón, M. A. Morón, L.Felipe Prieto-Martinez, M. Song, “Finite and infinite dimensional Lie group structures on Riordan groups”, Adv. Math., 319 (2017), 522–566  crossref  mathscinet  zmath  isi  scopus
    8. Grigorchuk R. de la Harpe P., “Amenability and Ergodic Properties of Topological Groups: From Bogolyubov Onwards”, Groups, Graphs and Random Walks, London Mathematical Society Lecture Note Series, 436, ed. CeccheriniSilberstein T. Salvatori M. SavaHuss E., Cambridge Univ Press, 2017, 215–249  mathscinet  zmath  isi
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