From the 1 of 5 linked papers with an AI index.
5 papers
Quantum Steenrod powers and Hamiltonian maps
Shaoyun Bai, Egor Shelukhin, Nicholas Wilkins +1
The paper proves new results about periodic points of Hamiltonian diffeomorphisms on closed symplectic manifolds, linking properties like pseudo‑rotations and symplectically degene…
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…
Equivariant Cerf theory and perturbative Casson invariants
Shaoyun Bai, Boyu Zhang
We develop an equivariant Cerf theory for Morse functions on finite-dimensional manifolds with group actions, and adapt the technique to the infinite-dimensional setting to study t…
Bordism and resolution of singularities
Mohammed Abouzaid, Shaoyun Bai
We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of…
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…