Holomorphic polygons and smooth 4-manifold invariants

2013/10/10 by Jonathan D. Williams, Williams, Jonathan D.
Mathematics · #57R17 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1310.2969

openalex publication_date 2013/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g>2 that specifies it up to diffeomorphism. The goal of this paper is to prove the following statement: For any smooth, closed oriented 4-manifold M, there is a sequence of weak A-infinity algebras indexed by g, and the homotopy equivalence class of each entry of this sequence is a diffeomorphism invariant of M.

Citations

• Holomorphic disks and topological invariants for closed three-manifolds
• Topology of broken Lefschetz fibrations and near-symplectic 4-manifolds

Related

• Holomorphic triangles and invariants for smooth four-manifolds
• An obstruction to smooth isotopy in dimension 4
• A note on homotopy and pseudoisotopy of diffeomorphisms of 4-manifolds
• Four-manifolds, two-complexes and the quadratic bias invariant
• Holomorphic triangle invariants and the topology of symplectic four-manifolds