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We introduce a new discretization of O'Hara's M\"obius energy. In contrast tothe known discretizations of Simon and Kim and Kusner it is invariant underM\"obius transformations of the surrounding space. The starting point for thisnew discretization is the cosine formula of Doyle and Schramm. We then show$\Gamma$-convergence of our discretized energies to the M\"obius energy undervery natural assumptions.

A M\"obius invariant discretization of O'Hara's M\"obius energy