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Rectification of circles and quaternions

Vladlen Timorin
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Abstract

Consider a bundle of circles passing through 0 in 4-dimensional space. It is said to be rectifiable if there is a germ of diffeomorphism at 0 that takes all circles from our bundle to straight lines. We will give a classification of all rectifiable bundles of circles containing sufficiently many circles in general position. This result is surprisingly different from those in dimensions 2 and 3(Khovanskii and Izadi) due to a connection with the quaternionic algebra.

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Vladlen Timorin. 2001-10-14. Rectification of circles and quaternions. https://arxiv.org/abs/math/0110144

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