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13.
Some totally real embeddings of three-manifolds
Forstnerič, Franc, 1958-
Naj bo ▫$V$▫ kompleksna hiperploskev v neki odprti podmnožici ▫$\mathbb C^3$▫, in naj bo ▫$M$▫ gladka kompaktna realna hiperploskev v ▫$V$▫. Z uporabo izreka M. L. Gromova dokažemo, da obstajajo ...majhne ▫$C^1$▫ perturbacije ▫$\widetilde{M}$▫ hiperploskve ▫$M$▫ v ▫$\mathbb C^3$▫, tako da je ▫$\widetilde{M}$▫ povsem realna podmnogoterost ▫$\mathbb C^3$▫. Kot posledico dokažemo, da lahko nekatere kvociente tridimenzionalne sfere povsem realno vložimo v ▫$\mathbb C^3$▫. V nekaterih primerih najdemo eksplicitne povsem realne vložitve, na primer za tridimenzionalni projektivni prostor. Naša konstrukcija je podobna Ahernovi in Rudinovi povsem realni vložitvi tridimenzionalne sfere v ▫$\mathbb C^3$▫.
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