On symmetries of spheres in univalent foundations

On symmetries of spheres in univalent foundations

Working in univalent foundations, we investigate the symmetries of spheres, i.e., the types of the form \(\mathbb{S}^n = \mathbb{S}^n\). The case of the circle has a slick answer: the symmetries of the circle form two copies of the circle. For higher-dimensional spheres, the type of symmetries has a...

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Veröffentlicht in:arXiv.org 2024-01
Hauptverfasser: Cagne, Pierre, Buchholtz, Ulrik, Kraus, Nicolai, Bezem, Marc
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Buchholtz, Ulrik
Kraus, Nicolai
Bezem, Marc
description Working in univalent foundations, we investigate the symmetries of spheres, i.e., the types of the form \(\mathbb{S}^n = \mathbb{S}^n\). The case of the circle has a slick answer: the symmetries of the circle form two copies of the circle. For higher-dimensional spheres, the type of symmetries has again two connected components, namely the components of the maps of degree plus or minus one. Each of the two components has \(\mathbb{Z}/2\mathbb{Z}\) as fundamental group. For the latter result, we develop an EHP long exact sequence.
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