BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Lisbeth Fajstrup (Aalborg University - Denmark)
DTSTART:20220819T150000Z
DTEND:20220819T160000Z
DTSTAMP:20260423T022804Z
UID:GEOTOP-A/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/21/
 ">Collapsing in directed topology</a>\nby Lisbeth Fajstrup (Aalborg Univer
 sity - Denmark) as part of GEOTOP-A seminar\n\n\nAbstract\nIn a simplicial
  complex\, a pair of simplices  are a collapsing pair\, if one is a unique
  maximal coface of the other which is then a free face. Such a pair can be
  collapsed by removal of the two simplices and all simplices between them 
 – think about an edge in a solid tetrahedron\; collapsing means removing
  the edge\, the interior of the tetrahedron and the interior of the two fa
 ces containing that edge. This leads to a homotopy equivalence. There is a
  similar notion for cubical complexes. A sequence of collapses leads to a 
 simpler (fewer simplices/cubes) space.\nFor a directed space\, which is a 
 topological space with a selected set of paths\, the directed paths\, dire
 cted homotopy equivalence is a very strong requirement\, and not what shou
 ld be the basis of collapsing.\nWe study the following setting: A Euclidea
 n Cubical Complex\, an ECC\, is a subset of R^n which is a union of elemen
 tary cubes. An elementary cube is a product of n intervals [ai\,ai+e]\, wh
 ere e is either 0 or 1. A directed path in an ECC is continuous and non-de
 creasing in all coordinates.\nWe define a notion of collapse with the aim 
 of preserving various properties of spaces of directed paths.\nThis is joi
 nt work with the WiT\, Women in Topology\, group R. Belton\, R. Brooks\, S
 .Ebli\, L.F.\, B.T.Fasy\, N.Sanderson\, E. Vidaurre.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/21/
END:VEVENT
END:VCALENDAR