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math.SG2026
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…
math.SG2026
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…
math.SG2026
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…