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A counter-example to Hausmann's conjecture
Virk, Žiga, 1982-
Leta 1995 je Hausmann dokazal, da je kompaktna Riemannova mnogoterost homotopsko ekvivalentna svojemu Ripsovemu kompleksu pri majhnih velikostnih parametrih. Nato je postavil domnevo, da je ...povezanost Ripsovih kompleksov monotona funkcija velikostnega parametra. Vsi dosedanji primeri so domnevo potrjevali. V članku dokažemo, da obstaja metrika na tridimenzionalni sferi, ki ne zadošča Hausmannovi domnevi. Dokaz vključuje stabilnostni izrek o vztrajnostni homologiji, vztrajnostni Hausmannov izrek ter aproksimacijski izrek Ferryja in Okuna.
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