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On intrinsic homological mirror symmetry for toric degenerations
Shaoyun Bai, Sebastian Haney
This paper studies the Floer-theoretic aspects of homological mirror symmetry inspired by proposals of Perutz and Siebert and the Gross--Siebert intrinsic mirror symmetry program.…
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…
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…
Equivariant formality in complex-oriented theories
Shaoyun Bai, Daniel Pomerleano
Let be a product of unitary groups and let be a compact symplectic manifold with Hamiltonian -action. We prove an equivariant formality result for any complex-orient…