Browsing by Author "Zaslow, E"

Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Augmentations are Sheaves
    Ng, L; Rutherford, D; Shende, V; Sivek, S; Zaslow, E
    We show that the set of augmentations of the Chekanov-Eliashberg algebra of a Legendrian link underlies the structure of a unital A-infinity category. This differs from the non-unital category constructed in [BC], but is related to it in the same way that cohomology is related to compactly supported cohomology. The existence of such a category was predicted by [STZ], who moreover conjectured its equivalence to a category of sheaves on the front plane with singular support meeting infinity in the knot. After showing that the augmentation category forms a sheaf over the x-line, we are able to prove this conjecture by calculating both categories on thin slices of the front plane. In particular, we conclude that every augmentation comes from geometry.
  • Thumbnail Image
    ItemOpen Access
    Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories
    (Nuclear Physics, Section B, 1995-12-25) Sethi, S; Stern, M; Zaslow, E
    We study the existence of monopole bound states saturating the BPS bound in N = 2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an L2 index theorem, we prove the existence of certain BPS states predicted by Seiberg and Witten based on their study of the vacuum structure of N = 2 Yang-Mills theories. © 1995.