Integral Kirwan Surjectivity

2024/10/08 by Daniel Pomerleano, Pomerleano, Daniel, Constantin Teleman +1
Mathematics · #Advanced Mathematical Theories #FOS: Mathematics #Mathematics and Applications #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2410.06197

openalex publication_date 2024/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We refine Kirwan's surjectivity and formality theorems for a Hamiltonian G-action on a compact symplectic manifold M. For a regular value of the moment map, we show that the Kirwan map is surjective and additively split after inverting the orders of stabilizers in the reduction. In particular, for a free quotient, it is surjective integrally. We generalize this to a splitting of MU-module spectra. We also give a stable version of Kirwan's equivariant formality theorem. The novel idea is to exploit the Atiyah-Bott argument in Morava K-theory, then return to bordism and cohomology.

Related

• Surjectivity for Hamiltonian G-spaces in K-theory
• Kirwan surjectivity in K-theory for Hamiltonian loop group quotients
• Equivariant formality in complex-oriented theories
• The Kirwan map, equivariant Kirwan maps, and their kernels
• The Kernel of the Equivariant Kirwan Map and the Residue Formula