Gorapada Bera will speak online in our geometry seminar on 09/28/2022. The talk is at 7pm on Teams. Gorapada’s title is “Associatives in twisted connected sums of G_2 manifolds” and his abstract is below.
G_2 manifolds are Riemannian manifolds whose holonomy contained in the exceptional Lie group G_2 and associatives inside them are some 3-dimensional calibrated submanifolds which play a crucial role for defining several enumerative theories of the G_2 manifolds. This motivates us to construct many examples of associatives. The most effective method to date of constructing G_2 manifolds is the twisted connected sum construction which glues a matching pair of asymptotically cylindrical (ACyl) G_2 manifold or ACyl Calabi-Yau 3-fold. In this talk we present a method to construct closed rigid (unobstructed) associatives in the twisted connected sum G_2-manifolds by gluing ACyl associatives in ACyl G_2-manifolds under a hypothesis which can be interpreted as a transverse Lagrangian intersection condition. We rewrite the gluing hypothesis for ACyl associatives obtained from ACyl holomorphic curves or ACyl special Lagrangian 3-folds in ACyl Calabi-Yau 3-folds. This helps us to construct many new associatives which are diffeomorphic to S^3, RP^3 or RP^3#RP^3.