This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.
This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers.
Algebraic topologists work with compactly generated spaces, CW complexes, or spectra. This book deals with homotopy theory, one of the main branches of algebraic topology.
Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.
In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes over a reasonable base scheme $k$.
The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc ...
Here E* is the dual of E and S(E*, i) stands for a graded symmetric algebra with E” in degree i and similarly A(E", ... More precisely Quillen considered the following category Ap(G): its Objects are the elementary abelian p-subgroups ...
This language was proposed by J. P. May in the 1970s to describe the structures on various loop spaces. This book presents a detailed study of the concept of an operad in the categories of topological spaces and of chain complexes.
Algebraic and Geometrical Methods in Topology: Conference on Topological Methods in Algebraic Topology, Suny, Binghamton, USA, Oct. 3-7, 1973
The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications in algebraic geometry as understood by Lawson and Voevodsky.
We also have a commutative diagram Esso (X) Eó, —- E;, o (X) (bá, lo. Ešo (X) Eó, —- Eš. Since b1, b2, ... form a simple system of generators for E:o c H.(B; R), it follows spoo is an isomorphism. Thus all the hypotheses of 15.57 ...