Symplectic semi-characteristics

2025/05/20 by Zhuang, Hao
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2505.14496

Abstract

We study the symplectic semi-characteristic of a 4n-dimensional closed symplectic manifold. First, we define the symplectic semi-characteristic using the mapping cone complex model of the primitive cohomology. Second, using a vector field with nondegenerate zero points, we prove a counting formula for the symplectic semi-characteristic. As corollaries, we obtain an Atiyah type vanishing property and the fact that the symplectic semi-characteristic is independent of the choices of symplectic forms.

Citations

• A vanishing property about the 1-filtered cohomology groups of (4n+2)-dimensional closed symplectic manifolds
• Analytic and topological realizations of the invariant Thom-Smale complex
• Symplectic Morse Theory and Witten Deformation

Related

• Uniqueness of symplectic canonical class, surface cone and symplectic cone of 4-manifolds with b⁺=1
• On certain geometric and homotopy properties of closed symplectic manifolds
• A vanishing property about the 1-filtered cohomology groups of (4n+2)-dimensional closed symplectic manifolds
• Characteristic Classes in Symplectic Topology
• Minimal models of compact symplectic semitoric manifolds