Higher homotopy invariants for spaces and maps

Blanc, David; Johnson, Mark W; Turner, James M

doi:10.2140/agt.2021.21.2425

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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

DOI: 10.2140/agt.2021.21.2425

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 $f : X \to Y$ which induce the same morphism $f_{*} : π_{*} X \to π_{*} Y$ .

Keywords

higher homotopy operation, homotopy invariants, $\Pi$–algebra, simplicial resolution

Mathematical Subject Classification 2010

Primary: 55Q35

Secondary: 18G30, 55P15, 55U35

References

Publication

Received: 20 November 2019

Revised: 29 October 2020

Accepted: 13 November 2020

Published: 31 October 2021

Authors

David Blanc
Department of Mathematics University of Haifa Haifa Israel

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

Volume 21, issue 5 (2021)