BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Francesca Tombari (KTH - Royal Institute of Technology) DTSTART:20251208T123000Z DTEND:20251208T133000Z DTSTAMP:20260422T140101Z UID:BilTop/129 DESCRIPTION:Title: Decompositions of tame parametrised chain complexes\nby Francesca Tom bari (KTH - Royal Institute of Technology) as part of Bilkent Topology Sem inar\n\nLecture held in SA 141.\n\nAbstract\nWe show a classification resu lt for tame filtered chain complexes with indexing posets of dimension 1. Filtered chain complexes\, on the one hand\, arise from filtrations of fin ite point clouds. On the other hand\, they are the cofibrant replacements of any tame parametrised chain complex\, once an appropriate model categor y structure is defined. Posets of dimension 1 form the other fundamental p iece of this presentation. Examples of these are given by natural\, intege r\, real numbers with the usual order\, trees and zigzags. \n\nOur classif ication result states that there are only two types of cofibrant (filtered ) indecomposables in the category tame(Q\, ch(C))\, where Q is a poset of dimension 1\, and C is an appropriate category. They are either disks (tri vial homology) of indecomposable projectives in tame(Q\, C) or spheres (no n-trivial homology) on the minimal projective resolution of the homology o f the chain complex. Both of them are nonzero in only two consecutive degr ees. If time allows\, we will also show a technique\, based on “glueing ”\, to construct indecomposables in a functor category by “smaller” indecomposables. Examples obtained in this way will also show that the res ults presented above\, for functors indexed by posets of dimension 1\, are not immediately generalisable. \n\nThis presentation is based on joint wo rk with Wojciech Chachólski\, Barbara Giunti and Claudia Landi.\n LOCATION:https://researchseminars.org/talk/BilTop/129/ END:VEVENT END:VCALENDAR