Abstract
This thesis concerns the computation of symplectic invariants of a special family of hypersurface singularities defined by polynomials fn;d : Cd ! C, indexed by positive integers n >= d. It studies connections between Lagrangian Floer theory and Auslander-Reiten theory for algebras of type A, associated to the linearly oriented An quiver.We compute the Fukaya-Seidel category associated to fn;d by explicitly describing generating objects. In the special case of curve singularities, we provide a complete description of the Milnor fibres. We use this construction to establish a derived equivalence between the Fukaya-Seidel categories of the family of singularities fn;d, and the partially wrapped Fukaya categories considered by Dyckerhoff-Jasso-Lekili and defined by Auroux. We provide explicit equivalences between the Fukaya-Seidel categories and the perfect derived categories of higher Auslander algebras of type A, indexed by positive integers n>=d and denoted by An;d.
We use our symplectic description of higher Auslander algebras of type A to provide a geometric interpretation of the recursive construction of An;d established by Iyama, which is based on higher Auslander correspondence.
| Date of Award | 1 Jan 2025 |
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| Original language | English |
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| Supervisor | Yanki Lekili (Supervisor) |