BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nick Scoville DTSTART:20260216T113000Z DTEND:20260216T133000Z DTSTAMP:20260423T005649Z UID:BNAT/14 DESCRIPTION:Title: A McCord theorem for (Čech) closure spaces\nby Nick Scoville as part of Basic Notions and Applied Topology Seminar\n\nLecture held in Room 1 at t he IMPAS\, Room 1.14 at the Institute of Informatics (University of Gdańs k).\n\nAbstract\nIn this talk\, we verify analogues of classical results f or higher homotopy groups and singular homology groups of (\\v{C}ech) clos ure spaces. Closure spaces are a generalization of topological spaces that also include graphs and directed graphs and are thus a bridge that connec ts classical algebraic topology with the more applied side of topology\, s uch as digital topology. Our main result is the construction of a weak hom otopy equivalence between the geometric realizations of (directed) Vietori s-Rips complexes and their underlying (directed) graphs. This implies that singular homology groups of finite graphs can be efficiently calculated f rom finite combinatorial structures\, despite their associated chain group s being infinite dimensional. This work is similar to the work McCord did for finite topological spaces\, but in the context of closure spaces. This is joint work with Nikolai Milicevic.\n LOCATION:https://researchseminars.org/talk/BNAT/14/ END:VEVENT END:VCALENDAR