Abstract:
A systematic description is given of properties of the group J(k) of formal power series in one variable with coefficients in a commutative unitary ring 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 J(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.
\Bibitem{Bab13}
\by I.~K.~Babenko
\paper Algebra, geometry, and topology of the~substitution group of formal power series
\jour Russian Math. Surveys
\yr 2013
\vol 68
\issue 1
\pages 1--68
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This publication is cited in the following 17 articles:
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I. A. Taimanov, “Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds”, Proc. Steklov Inst. Math., 327 (2024), 300–312
Sihao Tang, Weiping Wang, “Left multiplication operators on the Riordan group”, Advances in Applied Mathematics, 151 (2023), 102574
Ana Luzón, Manuel A. Morón, Luis Felipe Prieto-Martínez, “Commutators and commutator subgroups of the Riordan group”, Advances in Mathematics, 428 (2023), 109164
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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
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J. Mostovoy, J. M. Pérez-Izquierdo, I. P. Shestakov, “Nilpotent Sabinin algebras”, J. Algebra, 419 (2014), 95–123
I. Babenko, S. Bogatyi, “On topological properties of the formal power series substitution group”, Enseign. Math., 59:3-4 (2013), 271–286
V. M. Buchstaber, “Complex cobordism and formal groups”, Russian Math. Surveys, 67:5 (2012), 891–950
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