2012/11/01 by Kentaro Mikami, Mikami, Kentaro, Yasuharu Nakae +1
Mathematics · #57R17 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Primary 57R32 #Secondary 17B66 #Symplectic Geometry (math.SG) #math.AT #math.DG #math.SG #msc:17B66 #msc:57R17 #msc:57R32
paper · pdf · doi:10.48550/arxiv.1211.0185
133 pages
openalex publication_date 2012/11/01 · arxiv created 2014/04/28 · arxiv updated 2014/04/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we investigate the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R4. In the case of formal Hamiltonian vector fields on R2, we computed the relative Gel'fand-Kalinin-Fuks cohomology groups of weight <20 in the paper by Mikami-Nakae-Kodama. The main strategy there was decomposing the Gel'fand-Fucks cochain complex into irreducible factors and picking up the trivial representations and their concrete bases, and ours is essentially the same. By computer calculation, we determine the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R4 of weights 2, 4 and 6. In the case of weight 2, the Betti number of the cohomology group is equal to 1 at degree 2 and is 0 at any other degree. In weight 4, the Betti number is 2 at degree 4 and is 0 at any other degree, and in weight 6, the Betti number is 0 at any degree.