3 papers
math.SG2024
Cohomological splitting over rationally connected bases
Shaoyun Bai, Daniel Pomerleano, Guangbo Xu
We prove a cohomological splitting result for Hamiltonian fibrations over enumeratively rationally connected symplectic manifolds As a key application, we prove that the cohomology…
math.SG2024
Quantum Kirwan map and quantum Steenrod operation
Guangbo Xu
We construct an equivariant extension of the quantum Kirwan map and show that it intertwines the classical Steenrod operation on the cohomology of a classifying space with the quan…
math.SG2023
Franks' dichotomy for toric manifolds, Hofer-Zehnder conjecture, and gauged linear sigma model
Shaoyun Bai, Guangbo Xu
We prove that for any compact toric symplectic manifold, if a Hamiltonian diffeomorphism admits more fixed points, counted homologically, than the total Betti number, then it has i…