Infinite loop space theory

1977/01/01 by J. P. May · 1 citation
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Black Holes and Theoretical Physics #Algebraic structures and combinatorial models #Loop (graph theory) #Space (punctuation) #Mathematics #Topology (electrical circuits) #Computer science #Combinatorics

paper · pdf · doi:10.1090/s0002-9904-1977-14318-8

openalex publication_date 1977/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

Introduction. The notion of a generalized cohomology theory plays a central role in algebraic topology. Each such additive theory E* can be represented by a spectrum E. Here E consists of based spaces , for / > 0 such that E i is homeomorphic to the loop space tiE i+l of based maps S l - E i+ ,, and representability means that E n X = [X, E n ], the Abelian group of homotopy classes of based maps X -* E n , for n > 0. The existence of the E for i > 0 implies the presence of considerable internal structure on E 0 , the least of which is a structure of homotopy commutative //-space. Infinite loop space theory is concerned with the study of such internal structure on spaces.

Citations

• A general algebraic approach to steenrod operations
• Homotopy Invariant Algebraic Structures on Topological Spaces
• Categories and cohomology theories
• Genetics of Homotopy Theory and the Adams Conjecture
• Homotopy-everything 𝐻-spaces
• Cohomologie modulo 2 des complexes d’Eilenberg-MacLane
• The adams conjecture
• The nilpotency of elements of the stable homotopy groups of spheres
• The Geometry of Iterated Loop Spaces
• Theory of Braids
• Clifford modules
• On the groups J(X)—I

Cited by

• Operad [wikipedia]