Structured Ring Spectra (London Mathematical Society Lecture Note Series)
Contributors: Andrew Baker (Editor); Birgit Richter (Editor)
Publisher: Cambridge University Press
Published: November 22, 2004
Language: eng
Format: Paperback
Number of pages: 240
ISBN-13: 9780521603058
Subjects: Fields & rings; Science/Mathematics; Homotopy theory; Mathematics; Spectral theory (Mathematics); Algebra - General; Topology - General; Mathematics / Algebra / General; Categories (Mathematics); Rings (Algebra)
First sentence: The aim of this paper is to give some historical background to the first of the modern treatments of structured ring spectra: the S-module approach of [2].
Description: Within algebraic topology, the prominent role of multiplicative cohomology theories has led to a great deal of foundational research on ring spectra and in the 1990s this gave rise to significant new approaches to constructing categories of spectra and ring-like objects in them. This book contains some important new contributions to the theory of structured ring spectra as well as survey papers describing these and relationships between them. One important aspect is the study of strict multiplicative structures on spectra and the development of obstruction theories to imposing strictly associative and commutative ring structures on spectra. A different topic is the transfer of classical algebraic methods and ideas, such as Morita theory, to the world of stable homotopy.