Exact Lagrangian Submanifolds in T*Sn and the Graded Kronecker Quiver

Lagrangian non-intersections

“…M = CP n ) certain assumptions on H 1 (L; Z) of a Lagrangian L completely determine the entire homology of L. This phenomenon is illustrated in Theorems A-C of Section 1.1 below. Note that very recently examples of this phenomenon have been discovered also for cotangent bundles of spheres by Buhovski [10] and by Seidel [35]. The second phenomenon presented in this paper belongs to the framework of Lagrangian intersections.…”

Microlocal branes are constructible sheaves

“…The following application of the equivalence of F (T * X) and Sh c (X) generalizes part of the main statement of [32] from the case when X is a sphere. During the preparation of this paper, we learned that a similar characterization of compact exact branes has recently been obtained by Fukaya-Seidel-Smith [9,35] by a variety of different methods.…”

“…The question of the possible structure of compact Lagrangian submanifolds of T * X has seen some progress in recent years. For a recent example of the subject, we refer the reader to the paper of Seidel [32]. It contains a brief summary of other relevant works of Lalonde-Sikarov [26], Viterbo [38], and Buhovsky [4], and is the paper in the subject which is closest to this one in methods.…”

Exact Lagrangian submanifolds in simply-connected cotangent bundles

“…Surjectivity of the projection N → L was proved in one of the first papers on the subject [14]. Furthermore, many non-embedding results are known for special classes of manifolds N or L; besides the reference already quoted, see [24,25,23,3,9,21] (even this is a non-exhaustive list). Together, these papers use a wide variety of approaches, and the consequent statements vary considerably in strength (sometimes far outstripping what one can get by applying Theorem 1; for instance, results in [24] and [9] prove that every oriented exact L ⊂ T * S 2 is indeed Lagrangian isotopic to the zero-section).…”