Homological mirror symmetry for Rabinowitz Fukaya categories of Milnor fibers of Brieskorn-Pham singularities
Yanki Lekili, Kazushi Ueda
TL;DR
This paper establishes homological mirror symmetry for Rabinowitz Fukaya categories of Milnor fibers of certain singularities, enabling calculations of Rabinowitz Floer homology via Hochschild homology of matrix factorizations.
Contribution
It proves homological mirror symmetry for non-Calabi-Yau Brieskorn-Pham Milnor fibers, expanding the class of singularities where this duality is understood.
Findings
Homological mirror symmetry verified for specific Milnor fibers.
Rabinowitz Floer homology computed as Hochschild homology.
Extension of mirror symmetry results beyond Calabi-Yau cases.
Abstract
We discuss homological mirror symmetry for Rabinowitz Fukaya categories of Milnor fibers of invertible polynomials, and prove it for Brieskorn-Pham polynomials which are not of Calabi-Yau type. This allows a calculation of the Rabinowitz Floer homology of the Milnor fiber as the Hochschild homology of the dg category of equivariant matrix factorizations.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry