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Stable Algebraic Topology and Stable Topological Algebra
Author(s) -
May J. P.
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460939700427x
Subject(s) - mathematics , topology (electrical circuits) , algebraic topology , homotopy , algebraic number , general topology , subject (documents) , initial topology , computational topology , algebra over a field , extension topology , pure mathematics , topological space , computer science , combinatorics , mathematical analysis , scalar field , mathematical physics , library science
Algebraic topology is a young subject, and its foundations are not yet firmly in place. I shall give some history, examples and modern developments in that part of the subject called stable algebraic topology, or stable homotopy theory. This is by far the most calculationally accessible part of algebraic topology, although it is also the least intuitively grounded in visualizable geometric objects. It has a great many applications to other subjects such as algebraic geometry and geometric topology. Time will not allow me to say as much as I would like about that. Rather, I shall emphasize some foundational issues that have been central to this part of algebraic topology since the early 1960s, but that have been satisfactorily resolved only in the last few years. 1991 Mathematics Subject Classification 55P42, 55N20.