Constructing 𝑈𝑉^{𝑘}-maps between spheres

Ferry, Steven C.

doi:10.1090/S0002-9939-1994-1166355-5

Constructing $UV^ k$-maps between spheres
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by Steven C. Ferry

Proc. Amer. Math. Soc. 120 (1994), 329-332

DOI: https://doi.org/10.1090/S0002-9939-1994-1166355-5

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Abstract:

The purpose of this note is to give a quick proof of an extremely counterintuitive theorem of Bestvina, Walsh, and Wilson. The theorem says, for example, that the degree $2$ map ${d_2}:{S^3} \to {S^3}$ is homotopic to a map such that ${p^{ - 1}}(x)$ is connected for each $x \in {S^3}$.

References

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A general method of constructing

mappings on manifolds with applications to spheres

Simplicial spaces, nucleii, and

groups

45

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