2012/10/05 by Kentaro Mikami, Mikami, Kentaro, Hiroki Kodama +3 · 3 citations
Mathematics · #57R17 (Primary) 17B66 (Secondary) #57R32 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:17B66 #msc:57R17 #msc:57R32
paper · pdf · doi:10.48550/arxiv.1210.1662
20 pages
openalex publication_date 2012/10/05 · arxiv created 2014/02/19 · arxiv updated 2014/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In "The Gel'fand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations", arXiv:0910.3414, (October 2009) by D.Kotschick and S.Morita, the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields without constant vector fields on 2n-plane were characterized by two parameters, one is degree and the other is weight. And they obtained those cohomology groups of the 2-plane while their weight <= 10. In this paper, for those cohomology groups of the 2-plane, we succeeded in determining the dimension of cochain complexes by Sp(2,R)-representation theory for their weight even less than 50, thus, we manipulate the Euler characteristic numbers. We also decide our relative Gel'fand-Kalinin-Fuks cohomology groups until whose weight < 20 by getting a concrete matrix representation of the coboundary operator.