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arXiv · 1911.08259

Higher homotopy invariants for spaces and maps

David Blanc·Mark W. Johnson·James M. Turner
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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 $f_*$ from $\pi_* X$ to $\pi_* Y$.

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David Blanc, Mark W. Johnson, James M. Turner. 2019-11-19. Higher homotopy invariants for spaces and maps. https://doi.org/10.2140/agt.2021.21.2425

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