Higher Invariants for Spaces and Maps

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* : π*X→π*Y.

Find the version of record at https://doi.org/10.2140/agt.2021.21.2425

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Work Title Higher Invariants for Spaces and Maps
Access
Open Access
Creators
  1. David Blanc
  2. Mark W Johnson
  3. James M Turner
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Mathematical Sciences Publishers
Publication Date October 31, 2021
Publisher Identifier (DOI)
  1. 10.2140/agt.2021.21.2425
Source
  1. Algebraic & Geometric Topology
Deposited April 04, 2022

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  • Added Creator James M Turner
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    Description
    • 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*<sub>\</sub> : π<sub>\*</sub>X→π<sub>\*</sub>Y.
    • 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*<sub>\*</sub> : π<sub>\*</sub>X→π<sub>\*</sub>Y.
  • Updated