BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Thomas Fiedler DTSTART:20260801T140500Z DTEND:20260801T153500Z DTSTAMP:20260728T105610Z UID:knotgraphgroup/161 DESCRIPTION:Title: Detecting loops of singular long knots with polynomial complexity \nby Thomas Fiedler as part of Knots\, graphs and groups\n\n\nAbstract \nLet l be a loop of long knots with at least one ordinary double point an d which is given by a 1-parameter family of diagrams in the moduli space o f singular long knots. We assume that the Alexander polynomial for singula r knots is non trivial for the orientation preserving smoothing of at leas t one of the double points of the knot. We construct a 1-cocycle in the mo duli space and use it\, together with the efficient calculation of Alexand er polynomials for singular knots by Schut and van der Veen\, in order to determine the homology class represented by the loop l in the moduli space . Surprisingly\, this can be done with polynomial complexity with respect to the number of Reidemeister moves in the loop l and with respect to the maximal number of crossings of the knots in the loop.\n\nThis is research done with our working group of Louis Kauffman\, Sofia Lambropoulou\, Tumpa Mahato\, Kasturi Barkataki and Hamdi Kayaslan.\n LOCATION:https://researchseminars.org/talk/knotgraphgroup/161/ END:VEVENT END:VCALENDAR