2016/02/01 by Roger Casals, Viktor L. Ginzburg, Francisco Presas · 1 citation
Computer Science · Mathematics · #Algebra over a field #Class (philosophy) #Combinatorics #Computer science #Generalization #Geometric and Algebraic Topology #Group (periodic table) #Homogeneous #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Mathematical analysis #Mathematics #Pure mathematics #Quotient #Simple (philosophy) #Space (punctuation) #Symplectic geometry #Symplectic group #Symplectomorphism #Topological and Geometric Data Analysis #Transformation (genetics) #math.SG #msc:53D05 #msc:53D10
paper · pdf · doi:10.1016/j.geomphys.2016.03.021
published in Journal of Geometry and Physics 115, 167-177 (Elsevier BV)
arxiv created 2016/02/01 · openalex publication_date 2016/03/21 · arxiv updated 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We define Maslov--type indices associated to contact and symplectic transformation groups. There are two such families of indices. The first class of indices are maps from the homotopy groups of the contactomorphism or symplectomorphism group to a quotient of the integers. These are based on a generalization of the Maslov index. The second class of indices are maps from the homotopy groups of the space of contact structures or the space of cohomologous symplectic forms to the homotopy groups of a simple homogeneous space. We provide a detailed construction and describe some properties of these indices and their applications.