BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Emilio Minichiello (CUNY GC) DTSTART:20230404T203000Z DTEND:20230404T220000Z DTSTAMP:20260422T174056Z UID:tandg/4 DESCRIPTION:Title: Di ffeological Principal Bundles\, Čech Cohomology and Principal Infinity Bu ndles\nby Emilio Minichiello (CUNY GC) as part of Topology and Geometr y Seminar (Texas\, Kansas)\n\n\nAbstract\nThanks to a result of Baez and H offnung\, the category of diffeological spaces is equivalent to the catego ry of concrete sheaves on the site of cartesian spaces. By thinking of di ffeological spaces as kinds of sheaves\, we can therefore think of diffeol ogical spaces as kinds of infinity sheaves. We do this by using a model c ategory presentation of the infinity category of infinity sheaves on carte sian spaces\, and cofibrantly replacing a diffeological space within it. By doing this\, we obtain a new generalized cocycle construction for diffe ological principal bundles\, a new version of Čech cohomology for diffeol ogical spaces that can be compared very directly with two other versions a ppearing in the literature\, which is precisely infinity sheaf cohomology\ , and we show that the nerve of the category of diffeological principal G- bundles over a diffeological space X for a diffeological group G is weak e quivalent to the nerve of the category of G-principal infinity bundles ove r X.\n LOCATION:https://researchseminars.org/talk/tandg/4/ END:VEVENT END:VCALENDAR