Poincaré's stated motivations for topology
In the abstract of the paper, the authors say: ``It is well known that one of Poincaré's most important contributions to mathematics is the creation of algebraic topology. In this paper, the stated motivations of Poincaré and potential applications [\dots] for developing topology, are carefully mentioned. [\dots] This study will also shed some light on the broad interest of Poincaré in mathematics in a concrete way.'' In the introduction, the authors say: ``Poincaré's remark that `As for me, all the various ways in which I had engaged successively led me to Analysis Situs', can be the beginning of a major task to adequately understand how Poincaré saw the unity of mathematics in topology, and we hope to explore this question in the future.'' The paper consists of two parts: 1) Poincaré's stated motivations for topology in his publications from 1895 and 1901. 2) A critical analysis as to these. People being interested in these history and developments of the subject have to read this paper. It contains an encyclopaedic amount of material, let alone be itself but surely also its list of references. The authors provide the reader quotations of parts of letters of Poincaré to others, be it that these quotations are translations of the original French into English. [The original French texts of it are not to be found in the paper.] The overall impression of this paper is that, as said before, it is encyclopaedic, but at the tame highly informative. As such, a storehouse of interesting facts! Highly recommended and indispensable. Developments occurring in the ``second half'' of the 20th century have also been treated in detail, especially regarding groups of Lie-type.
finite and discrete subgroups of Lie groups
scientific article; zbMATH DE number 7219772
scientific article