By A. D. Elmendorf, I. Kriz, M. A. Mandell, J. P. May, and M. Cole

ISBN-10: 0821843036

ISBN-13: 9780821843031

This e-book introduces a brand new point-set point method of solid homotopy idea that has already had many functions and gives you to have a long-lasting influence at the topic. Given the sphere spectrum $S$, the authors build an associative, commutative, and unital wreck product in a whole and cocomplete type of "$S$-modules" whose derived class is such as the classical strong homotopy classification. This development permits an easy and algebraically conceivable definition of "$S$-algebras" and "commutative $S$-algebras" in phrases of associative, or associative and commutative, items $R\wedge _SR \longrightarrow R$. those notions are primarily similar to the sooner notions of $A_{\infty }$ and $E_{\infty }$ ring spectra, and the older notions feed obviously into the recent framework to supply considerable examples. there's an both easy definition of $R$-modules when it comes to maps $R\wedge _SM\longrightarrow M$. while $R$ is commutative, the class of $R$-modules additionally has an associative, commutative, and unital spoil product, and its derived class has homes like the strong homotopy classification. those structures let the importation into sturdy homotopy conception of loads of point-set point algebra.