Cycles Cross Ratio: an Invitation
arXiv:2105.05634 · doi:10.4171/EM/471
Abstract
The paper introduces cycles cross ratio, which extends the classic cross ratio of four points to various settings: conformal geometry, Lie spheres geometry, etc. Just like its classic counterpart cycles cross ratio is a measure of anharmonicity between spheres with respect to inversion. It also provides a Möbius invariant distance between spheres. Many further properties of cycles cross ratio awaiting their exploration. In abstract framework the new invariant can be considered in any projective space with a bilinear pairing.
10 pages, 3 PDF files in two figures, AMS-LaTeX; v2: Steiner power is linked to cross-ratio; v3: Jupyter notebook linked; v4: numerous improvements; v5: a couple of references is added; v6: minor corrections