Volume 21, issue 5 (2021)

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Higher homotopy invariants for spaces and maps

David Blanc, Mark W Johnson and James M Turner

Algebraic & Geometric Topology 21 (2021) 2425–2488

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 : X Y which induce the same morphism f: πX πY.

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higher homotopy operation, homotopy invariants, $\Pi$–algebra, simplicial resolution
Mathematical Subject Classification 2010
Primary: 55Q35
Secondary: 18G30, 55P15, 55U35
Received: 20 November 2019
Revised: 29 October 2020
Accepted: 13 November 2020
Published: 31 October 2021
David Blanc
Department of Mathematics
University of Haifa
Mark W Johnson
Department of Mathematics and Statistics
Penn State Altoona
Altoona, PA
United States
James M Turner
Department of Mathematics
Calvin University
Grand Rapids, MI
United States