Abstract
We study Dehn twists along Lagrangian submanifolds that are finite free quotients of spheres. We describe the induced auto-equivalences to the derived Fukaya category and explain their relations to mirror symmetry.
Highlights
In his early groundbreaking papers [1,2], Seidel studied the Dehn twist along a Lagrangian sphere and its induced auto-equivalence on the derived Fukaya category
Lagrangian Dehn twists along spheres can be generalized to submanifolds whose geodesics are all closed with the same period
When the Lagrangian submanifold is a complex projective space, Huybrechts and Thomas conjectured that the resulting symplectomorphism induces a P-twist in the Fukaya category [5]
Summary
In his early groundbreaking papers [1,2], Seidel studied the Dehn twist along a Lagrangian sphere and its induced auto-equivalence on the derived Fukaya category. When the Lagrangian submanifold is a complex projective space, Huybrechts and Thomas conjectured that the resulting symplectomorphism induces a P-twist in the Fukaya category [5]. Question 1.1 On a Fukaya category, what is the induced auto-equivalence of the Dehn twist along a spherical Lagrangian, i.e. a Lagrangian submanifold P whose universal cover is Sn?. Page 3 of 85 68 an entire family of previously unknown auto-equivalences We hope this result contributes to the increasing interests in studying derived categories and Fukaya categories of finite characteristics.
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