Higher homotopy invariants for spaces and maps

Abstract

For a pointed topological space $X$, we use an inductive construction of a simplicial resolution of $X$ by wedges of spheres to construct a "higher homotopy structure" for $X$ (in terms of chain complexes of spaces). This structure is then used to define a collection of higher homotopy invariants which suffice to recover $X$ up to weak equivalence. It can also be used to distinguish between different maps $f$ from $X$ to $Y$ which induce the same morphism on homotopy groups $f_{\ast }$ from ${\pi }_{\ast }X$ to ${\pi }_{\ast }Y$.

51 pages

References in corpus (2)

• Algebraic invariants for homotopy types
• On realizing diagrams of Pi-algebras

Cited by in corpus (2)

• Spectral Sequences in $(\infty ,1)$-Categories
• The higher structure of unstable homotopy groups