BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gabor Etesi (Budapest University of Technology and Economics) DTSTART:20250312T190000Z DTEND:20250312T200000Z DTSTAMP:20260420T053556Z UID:NYC-NCG/186 DESCRIPTION:Title: The four dimensional smooth Poincare conjecture from the viewpoint of Ne umann algebra representations\nby Gabor Etesi (Budapest University of Technology and Economics) as part of Noncommutative geometry in NYC\n\n\nA bstract\nIn this talk we outline the construction and basic properties of\ na new smooth 4-manifold invariant obtained by the aid of the rich\nrepres entation theory of the hyperfinite II_1 factor von Neumann algebra.\nThis invariant gives rise to a unital Abelian semigroup homomorphism from\n(the category of) connected compact oriented smooth 4-manifold equipped\nwith the connected sum operation into the semi-open interval [0\,1) with\nAbeli an semigroup operation $(s\,t)\\mapsto s+t-st$. This invariant has the\nin teresting property that its range is appropriately restricted by the\nposs ible values of Jones' indices of subfactors within the II_1\nhyperfinite f actor hence consists of a discrete and a continuous part. It\nis then obse rved that (i) the invariant is not injective on its continuous\nrange part \; (ii) when evaluated on the standard 4-sphere its value falls\nwithin th e discrete part of the range and its injectivity at this specific\nvalue i s equivalent to the validity of the 4 dimensional smooth Poincare\nconject ure. Moreover\, as the punch line of this talk\, it is expected that\nthis invariant possesses a sort of continuity hence non-invertability at\nits specifec values in the continuous range will imply non-invartability\nat n earby values\; however such argument cannot be applied to study the 4\ndim ensional smooth Poincare conjecture because of the aforementioned\ndiscret eness hence the conjecture's difficulty might be related with\nthe isolati on of the 4-sphere in this sense from the rest of smooth\n4-manifolds.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/186/ END:VEVENT END:VCALENDAR