2019/05/20 by Shuhei Maruyama, Maruyama, Shuhei
Environmental Science · #FOS: Mathematics #Geometric Topology (math.GT) #Methane Hydrates and Related Phenomena #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1905.08029
openalex publication_date 2019/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let D be a 2-dimensional closed unit disk and \rmSymp(D,0)_\rmrel the group of symplectomorphisms preserving the origin and the boundary ∂ D pointwise. We consider the ℝ-valued flux homomorphism on \rmSymp(D,0)_\rmrel and define the central ℝ-extension called the ℝ-valued flux extension. We determine the Euler class of this extension and investigate the relation between the extension, the group 2-cocycle defined by Ismagilov, Losik, and Michor, and the Calabi invariant of D.