7 citations · 37 across the 26 of their papers we have counts for
26 papers
A proof of the Arnold-Givental conjecture
Shaoyun Bai, Egor Shelukhin, Yi Wang +1
We prove the Arnold-Givental conjecture in full generality: given a closed symplectic manifold , an anti-symplectic involution with fixed point set $L={\rm F…
Quantum Steenrod powers and Hamiltonian maps
Shaoyun Bai, Egor Shelukhin, Nicholas Wilkins +1
We prove a series of new results in Hamiltonian dynamics on a general closed symplectic manifold , including: 1. If admits a Hamiltonian diffeomorphism which is either…
Integral Hamiltonian Floer theory: Foundations
Shaoyun Bai, Guangbo Xu
Continuing our previous work on the integral Arnold conjecture, we establish the foundation of Hamiltonian Floer theory over integer coefficients on any compact symplectic manifold…
Gauged linear sigma model in geometric phase. II. the virtual cycle
Gang Tian, Guangbo Xu
We provide the detailed construction of the virtual cycles needed for defining the cohomological field theory associated to a gauged linear sigma model in geometric phase.
Arnold conjecture over integers
Shaoyun Bai, Guangbo Xu
For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number ove…
A new transversality condition on orbifolds and integer-valued Gromov-Witten type invariants
Shaoyun Bai, Guangbo Xu
Following a proposal of Fukaya-Ono and the exploration by B. Parker, we introduce a new transversality condition, the FOP transversality condition, for sections of orbifold vector…
Counting pointlike instantons virtually without gluing
Gang Tian, Guangbo Xu
We use the first author's idea on "constructing virtual fundamental cycles without gluing ' to define the quantum correction term between the gauged linear sigma model and the nonl…
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…
A Compactness Theorem for Anti-Self-Dual Equation with Translation Symmetry
Guangbo Xu
Motivated by the Atiyah-Floer conjecture, we consider Santi-self-dual instantons on the product of the real line and a three-manifold with cylindrical end. We prove a Gromo…
A wall-crossing formula and the invariance of GLSM correlation functions
Gang Tian, Guangbo Xu
In this paper we prove a wall-crossing formula, a crucial ingredient needed to prove that the correlation function of gauged linear sigma model is independent of the choice of pert…
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.
Gauged Linear Sigma Model in Geometric Phases. I
Gang Tian, Guangbo Xu
We construct a cohomological field theory for a gauged linear sigma model space in geometric phase, using the method of gauge theory and differential geometry. The cohomological fi…
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…
The symplectic approach of gauged linear -model
Gang Tian, Guangbo Xu
Witten's Gauged Linear -Model (GLSM) unifies the Gromov-Witten theory and the Landau-Ginzburg theory, and provides a global perspective on mirror symmetry. In this article, we s…
Gluing affine vortices
Guangbo Xu
We construct a gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition at a rigid, regular, codimension one configuration. This const…
Virtual cycles of gauged Witten equation
Gang Tian, Guangbo Xu
We construct virtual cycles on moduli spaces of perturbed gauged Witten equation over a fixed smooth r -spin curve, under the framework of [TX15]. Together with the wall-crossing f…
Local model for the moduli space of affine vortices
Sushmita Venugopalan, Guangbo Xu
We show that the moduli space of regular affine vortices, which are solutions of the symplectic vortex equation over the complex plane, has the structure of a smooth manifold. The…
Gauged Floer homology and spectral invariants
Weiwei Wu, Guangbo Xu
We define a version of spectral invariant in the vortex Floer theory for a -Hamiltonian manifold . This defines potentially new (partial) symplectic quasi-morphism and quasi-…
Compactness in the adiabatic limit of disk vortices
Dongning Wang, Guangbo Xu
This paper is the first input towards an open analogue of the quantum Kirwan map. We consider the adiabatic limit of the symplectic vortex equation over the unit disk for a Hamilto…
Correlation functions of gauged linear -model
Gang Tian, Guangbo Xu
This is the second paper in a series following arXiv:1405.6352, on the construction of a mathematical theory of the gauged linear -model (GLSM). In this paper, assuming the exis…
Analysis of gauged Witten equation
Gang Tian, Guangbo Xu
The gauged Witten equation was essentially introduced by Witten in his formulation of gauged linear -model (GLSM). GLSM is a physics theory which explains the so-called Landau-G…
Gauged Hamiltonian Floer homology I: definition of the Floer homology groups
Guangbo Xu
We construct the vortex Floer homology group for an aspherical Hamiltonian -manifold with moment map and a class of -invariant Hamiltonian loop $H_…
Morse theory for Lagrange multipliers and adiabatic limits
Stephen Schecter, Guangbo Xu
Given two Morse functions on a compact manifold , we study the Morse homology for the Lagrange multiplier function on which sends to $f(x)…
U(1)-vortices and quantum Kirwan map
Guangbo Xu
We study the symplectic vortex equation over the complex plane, for the target space () with diagonal U(1)-action. We classify all solutions with finite en…