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A parity constraint on the topological numbers of self-complementary triply-periodic surfaces
The stability zone of Novikov's problem of planar sections of triply periodic surfaces are labeled by indivisible triples of integers, which we call the soul of the zone. Which triples may occur is not known. We show that, if a Morse function $f$ on $\mathbb T^3$ admits a translation $τ(x)=x+v$ with
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