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CATEGORIES:Academic Lectures and Seminars
DESCRIPTION:Ciprian Manolescu\, Professor\, Stanford University\n\n \n\nAbs
tract: Over the last forty years\, most progress in four-dimensional topolo
gy came from gauge theory and related invariants. Khovanov homology is an i
nvariant of knots in R^3 of a different kind: its construction is combinato
rial\, and connected to ideas from representation theory. There is hope tha
t it can tell us more about smooth 4-manifolds\; for example\, Freedman\, G
ompf\, Morrison and Walker suggested a strategy to disprove the 4D Poincare
conjecture using Rasmussen's invariant from Khovanov homology. It is yet u
nclear whether their strategy can work\, and I will explain some of its cha
llenges. (This is based on joint work with Lisa Piccirillo.) I will also re
view other topological applications of Khovanov homology\, including a rece
nt detection result for some exotic compact 4-manifolds with boundary (work
of Ren and Willis).
DTEND:20240404T213000Z
DTSTAMP:20240524T000941Z
DTSTART:20240404T203000Z
LOCATION:Palmer Engineering\, 104
SEQUENCE:0
SUMMARY:MATH: Colloquium: Khovanov homology and four-manifolds
UID:tag:localist.com\,2008:EventInstance_46006102207987
URL:https://events.unr.edu/event/math-colloquium-khovanov-homology-and-four
-manifolds
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