BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Basak Kucuk (University of Göttingen) DTSTART:20250711T103000Z DTEND:20250711T113000Z DTSTAMP:20260422T140237Z UID:BilTop/119 DESCRIPTION:Title: The Conjecture of Klein and Williams for the Equivariant Fixed Point Prob lem\nby Basak Kucuk (University of Göttingen) as part of Bilkent Topo logy Seminar\n\nLecture held in SA 141.\n\nAbstract\nKlein and Williams de veloped an obstruction theory for the homotopical equivariant fixed point problem\, which asks whether an equivariant map can be deformed\, through an equivariant homotopy\, to a map with no fixed points [KW\, Theorem H]. An alternative approach was given by Fadell and Wong [FW]\, using a collec tion of Nielsen numbers. The Nielsen number is a finer invariant than the Lefschetz number in the sense that it provides a converse to the Lefschetz fixed point theorem. Klein and Williams [KW] conjectured that these Niels en numbers could be computed from their invariant.\nIn this talk\, we pres ent our findings on this conjecture by providing an explicit decomposition of the Klein–Williams invariant under the tom Dieck splitting. We furth er discuss the application of the equivariant fixed point problem to the p eriodic point problem of period n. In this setting\, we show that the Klei n–Williams invariant and the Nielsen numbers N(fk)\, for all k dividing n\, carry the same amount of information. However\, they are not exactly t he same invariants\, and if time permits\, we will conclude with an explic it example illustrating this difference.\nReferences:\n[KW] J. R. Klein a nd B. Williams\, Homotopical intersection theory II\, Math. Z. 264 (2010). \n[FW] E. Fadell and P. Wong\, On deforming G-maps to be fixed point free \, Pacific Journal of Mathematics 132 (1988).\n LOCATION:https://researchseminars.org/talk/BilTop/119/ END:VEVENT END:VCALENDAR