41 citations · 176 across the 10 of their papers we have counts for
10 papers
Constructing the relative Fukaya category
Timothy Perutz, Nick Sheridan
We give a definition of Seidel's `relative Fukaya category', for a smooth complex projective variety, under a semipositivity assumption. We use the Cieliebak--Mohnke approach to tr…
Automatic split-generation for the Fukaya category
Timothy Perutz, Nick Sheridan
We prove a structural result in mirror symmetry for projective Calabi--Yau (CY) manifolds. Let be a connected symplectic CY manifold, whose Fukaya category is…
Mirror symmetry: from categories to curve counts
Sheel Ganatra, Timothy Perutz, Nick Sheridan
We work in the setting of Calabi-Yau mirror symmetry. We establish conditions under which Kontsevich's homological mirror symmetry (which relates the derived Fukaya category to the…
Arithmetic mirror symmetry for the 2-torus
Yanki Lekili, Timothy Perutz
This paper explores a refinement of homological mirror symmetry which relates exact symplectic topology to arithmetic algebraic geometry. We establish a derived equivalence of the…
Fukaya categories of the torus and Dehn surgery
Yanki Lekili, Timothy Perutz
This paper is a companion to the authors' forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted F…
A symplectic Gysin sequence
Timothy Perutz
We use the theory of pseudo-holomorphic quilts to establish a counterpart, in symplectic Floer homology, to the Gysin sequence for the homology of a sphere-bundle. In a motivating…