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Schedule


Date
Speaker
Title
Jan 30, 2pm
Yikai Teng (Rutgers University-Newark)
 Khovanov homology and exotic planes

 

Abstracts

Jan 30: Yikai Teng (Rutgers Univerity-Newark) "Khovanov homology and exotic planes"

Since the 1980s, mathematicians have discovered uncountably many "exotic" embeddings of R^2 in R^4, i.e., embeddings that are topologically but not smoothly isotopic to the standard xy-plane. However, until today, there have been no direct, computable invariants that could detect such exotic behavior (with prior results relying on indirect arguments). In this talk, we define the end Khovanov homology, which is the first known combinatorial invariant of properly embedded surfaces in R^4 up to ambient diffeomorphism. Moreover, we apply this invariant to detect new exotic planes, including the first known example of an exotic plane that is a Lagrangian submanifold of the standard symplectic R^4.