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The space of intervals in a Euclidean space
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For a path-connected space X, a well-known theorem of Segal, May and Milgram asserts that the configuration space of finite points in R^n with labels in X is weakly homotopy equivalent to the n-th loop-suspension of X. In this paper, we introduce a space I_n(X) of intervals suitably topologized in R^n with labels in a space X and show that it is weakly homotopy equivalent to n-th loop-suspension of X without the assumption on path-connectivity.
Forward citations
Cited by 2 Pith papers
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Fractional Quantum Hall Anyons via the Algebraic Topology of Exotic Flux Quanta
Fractional quantum Hall anyons are re-derived from a non-Lagrangian flux quantization in 2-Cohomotopy, with new predictions for torus degeneracy and defect anyons.
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Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization
Choosing equivariant twistorial Cohomotopy as the flux quantization law on single M5-probes wrapped on a Z2-orbifold yields abelian anyonic quantum states on the orbifold fixed locus.
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