Augmentation and sheaf categories for Legendrian knots

Augmentation and sheaf categories for Legendrian knots

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Lenhard Ng , Duke University
Fine Hall 314

Recently Vivek Shende, David Treumann, and Eric Zaslow introduced a category of constructible sheaves associated to a Legendrian knot, and conjectured that it is equivalent to a category built from augmentations of Legendrian contact homology. In joint work in progress with Dan Rutherford, Steven Sivek, Shende, and Zaslow, it now appears that we can prove this conjecture. I'll describe both categories, with emphasis on the definition and properties of the augmentation category, and perhaps gesture toward the proof of their equivalence.