2024/05/09 by Shaoyun Bai, Daniel Pomerleano, Bai, Shaoyun +1
Business, Management and Accounting · Computer Science · #Advanced Algebra and Logic #Advanced Computational Techniques and Applications #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Optics and Image Analysis #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2405.05821
openalex publication_date 2024/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a product of unitary groups and let (M,ω) be a compact symplectic manifold with Hamiltonian G-action. We prove an equivariant formality result for any complex-oriented cohomology theory 𝔼^* (in particular, integral cohomology). This generalizes the celebrated result of Atiyah-Bott-Kirwan for rational cohomology from the 1980s. The proof does not use classical ideas but instead relies on a recent cohomological splitting result of Abouzaid-McLean-Smith for Hamiltonian fibrations over \mathbbCP1. Moreover, we establish analogues of the "localization" and "injectivity to fixed points" theorems for certain cohomology theories studied by Hopkins-Kuhn-Ravenel. As an application of these results, we establish a Goresky-Kottwitz-MacPherson theorem with Morava K-theory coefficients for Hamiltonian T-manifolds.