Hopf quotients of the infinite-dimensional Gaussian pyramid

Takashi Shioya; Shigeaki Yokota

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arXiv · 2609.07030

Hopf quotients of the infinite-dimensional Gaussian pyramid

Takashi Shioya·Shigeaki Yokota

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Abstract

We study the infinite-dimensional Gaussian pyramid and its quotients by the global sign flip and the $U(1)$-Hopf action. We resolve affirmatively a long-standing problem posed by Tomohiro Fukaya around 2014: these three limiting geometries are pairwise non-similar, meaning that no positive rescaling makes any two of them coincide.

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Takashi Shioya, Shigeaki Yokota. 2026-09-07. Hopf quotients of the infinite-dimensional Gaussian pyramid. https://arxiv.org/abs/2609.07030

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