77 citations · 394 across the 48 of their papers we have counts for
30 papers · 1 filter
Fukaya categories of blowups
Sushmita Venugopalan, Chris T. Woodward, Guangbo Xu
We compute the Fukaya category of the symplectic blowup of a compact rational symplectic manifold at a point in the following sense: Suppose a collection of Lagrangian branes satis…
Tropical Fukaya Algebras
Sushmita Venugopalan, Chris Woodward
We introduce a tropical version of the Fukaya algebra of a Lagrangian submanifold. Tropical graphs arise as large-scale behavior of pseudoholomorphic disks under a multiple cut ope…
Partly-local domain-dependent almost complex structures
Guangbo Xu, Chris T. Woodward
We fill a gap pointed out by N. Sheridan in the proof of independence of genus zero Gromov-Witten invariants from the choice of divisor in the Cieliebak-Mohnke perturbation scheme.
Invariance of immersed Floer cohomology under Lagrangian surgery
Joseph Palmer, Chris Woodward
We show that Floer cohomology of an immersed Lagrangian brane is invariant under smoothing of a self-intersection point if the quantum valuation of the weakly bounding cochain vani…
An open quantum Kirwan map
Chris Woodward, Guangbo Xu
We construct a morphism from the equivariant Fukaya algebra of a Lagrangian brane in the zero level set of a moment map of a Hamiltonian action to the Fukaya algebra of the quotien…
Invariance of Immersed Floer cohomology under Maslov flows
Joseph Palmer, Chris Woodward, with an erratum written jointly with Hadi Azizi
We show that immersed Lagrangian Floer cohomology in compact rational symplectic manifolds is invariant under Maslov flows such as coupled mean curvature/Kaehler-Ricci flow in the…
Floer field theory for coprime rank and degree
Katrin Wehrheim, Chris Woodward
We construct partial category-valued field theories in (2+1)-dimensions using Lagrangian Floer theory in moduli spaces of central-curvature unitary connections with fixed determina…
A-infinity functors for Lagrangian correspondences
S. Ma'u, K. Wehrheim, C. Woodward
We construct A-infinity functors between Fukaya categories associated to monotone Lagrangian correspondences between compact symplectic manifolds. We then show that the composition…
Floer theory and flips
François Charest, Chris T. Woodward
We show that blow-ups or reverse flips (in the sense of the minimal model program) of rational symplectic manifolds with point centers create Floer-non-trivial Lagrangian tori. As…
Fukaya algebras via stabilizing divisors
François Charest, Chris Woodward
We use the technique of stabilizing divisors introduced by Cieliebak-Mohnke to construct finite dimensional, strictly unital Fukaya algebras of compact, oriented, relatively spin L…
Orientations for pseudoholomorphic quilts
Katrin Wehrheim, Chris Woodward
We construct orientations on moduli spaces of pseudoholomorphic quilts with seam conditions in Lagrangian correspondences equipped with relative spin structures and determine the e…
Floer field theory for tangles
Katrin Wehrheim, Chris Woodward
We use quilted Floer theory to construct functor-valued invariants of tangles arising from moduli spaces of flat bundles on punctured surfaces. As an application, we show the non-t…
Exact triangle for fibered Dehn twists
Katrin Wehrheim, Chris Woodward
We use quilted Floer theory to generalize Seidel's long exact sequence in symplectic Floer theory to fibered Dehn twists. We then apply it to construct versions of the Floer and Kh…
Floer trajectories and stabilizing divisors
François Charest, Chris Woodward
We incorporate pearly Floer trajectories into the transversality scheme for pseudoholomorphic maps introduced by Cieliebak-Mohnke. By choosing generic domain-dependent almost compl…
Quasimap Floer cohomology and varying symplectic quotients
Glen Wilson, Chris Woodward
We use quasimap Floer cohomology for varying symplectic quotients to resolve several puzzles regarding displaceability of toric moment fibers. For example, we (i) present a compact…
Quilted Floer trajectories with constant components
Katrin Wehrheim, Chris T. Woodward
We fill a gap in the proof of the transversality result for quilted Floer trajectories in arXiv:0905.1370 by addressing trajectories for which some but not all components are const…
Gauged Floer theory of toric moment fibers
Chris Woodward
We investigate the small area limit of the gauged Lagrangian Floer cohomology of Frauenfelder. The resulting cohomology theory, which we call quasimap Floer cohomology, is an obstr…
Moment maps and geometric invariant theory
Christopher T. Woodward
These lectures centered around the Kempf-Ness theorem, which describes the equivalence between notions of quotient in symplectic and algebraic geometry. The text also describes con…
Gauged Gromov-Witten theory for small spheres
Eduardo Gonzalez, Chris Woodward
For smooth projective G-varieties, we equate the gauged Gromov-Witten invariants for sufficiently small area and genus zero with the invariant part of equivariant Gromov-Witten inv…
Quilted Floer Cohomology
Katrin Wehrheim, Chris Woodward
We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish…
Pseudoholomorphic Quilts
Katrin Wehrheim, Chris Woodward
We define relative Floer theoretic invariants arising from 'quilted pseudo-holomorphic surfaces': Collections of pseudoholomorphic maps to various target spaces with 'seam conditio…
Floer Cohomology and Geometric Composition of Lagrangian Correspondences
Katrin Wehrheim, Chris T. Woodward
We prove an isomorphism of Floer cohomologies under geometric composition of Lagrangian correspondences in exact and monotone settings.
Deformations of symplectic vortices
Eduardo Gonzalez, Chris Woodward
We prove a gluing theorem for a symplectic vortex on a compact complex curve and a collection of holomorphic sphere bubbles. Using the theorem we show that the moduli space of regu…
Quantum Witten localization and abelianization for qde solutions
Eduardo Gonzalez, Chris Woodward
We prove a quantum version of the localization formula of Witten that relates invariants of a git quotient with the equivariant invariants of the action. Using the formula we prove…