A short proof of the generalized Conway--Gordon--Sachs theorem

Ryo Nikkuni

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arXiv · 2502.05930

A short proof of the generalized Conway--Gordon--Sachs theorem

Ryo Nikkuni

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Abstract

The famous Conway--Gordon--Sachs theorem for the complete graph on six vertices was extended to the general complete graph on $n$ vertices by Kazakov--Korablev as a congruence modulo $2$, and its integral lift was given by Morishita--Nikkuni. However, the proof is complicated and long. In this paper, we provide a shorter proof of the generalized Conway--Gordon--Sachs theorem over integers.

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Ryo Nikkuni. 2025-02-09. A short proof of the generalized Conway--Gordon--Sachs theorem. https://arxiv.org/abs/2502.05930

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