Rips complexes as nerves and a functorial Dowker-nerve diagram
Virk, Žiga, 1982-
Z uporabo ideje o Dowkerjevi dualnosti dokažemo, da je Ripsov kompleks pri parametru ▫$r$▫ homotopsko ekvivalenten živcu pokritja sestavljenega iz množic določenega diametra. Razvijemo funktorialno ...verzijo izreka o živcu z dodatkom Dowkerjeve dualnosti, s čemer dobimo funktorialen diagram Dowker-živec. Dobljene rezultate vključimo v sistematično obravnavo filtracij, ki izhajajo iz pokritij. Kot posledico dobimo spločen pristop k rekostrukciji prostorov z Ripsovimi kompleksi, kratek dokaz Hausmannovega rekonstrukcijskega izreka ter povsem klasificiramo rekonstrukcijske nivoje metričnih grafov. Poleg tega predstavimo novo metodo ekstrakcije homologije prostora, osnovano na vgnezdenih Ripsovih kompleksih na enem samem nivoju, ki je neodvisna od sosednjih nivojev in evklidske strukture ambientnega prostora.
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