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Algebraic and Geometric Topology


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.

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Mathematics Commons



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