TAILIEUCHUNG - Symplectic groupoids and generalized almost subtangent manifolds

We obtain equivalent assertions among the integrability conditions of generalized almost subtangent manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form, and generalized subtangent maps. | Turkish Journal of Mathematics Research Article Turk J Math (2015) 39 ¨ ITAK ˙ c TUB ⃝ doi: Symplectic groupoids and generalized almost subtangent manifolds ˙ ∗ Fulya S ¸ AHIN ˙ onu University, Malatya, Turkey Department of Mathematics, Faculty of Science and Art, In¨ Received: • Accepted: • Published Online: • Printed: Abstract: We obtain equivalent assertions among the integrability conditions of generalized almost subtangent manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form, and generalized subtangent maps. Key words: Lie groupoid, symplectic groupoid, generalized almost subtangent manifold 1. Introduction The concept of groupoid was introduced by Ehresmann [5] in the 1950s, following his work on the concept of principal bundle. A groupoid G consists of 2 sets G1 and G0 , called arrows and objects, respectively, with maps s, t : G1 → G0 called source and target. It is equipped with a composition m : G2 → G1 defined on the subset G2 = {(g, h) ∈ G1 × G1

• Toán học
• Lie groupoid
• Symplectic groupoid
• Generalized almost subtangent manifold
• Generalized subtangent maps
• Symplectic groupoids
• Generalized almost paracomplex manifold
• Paraholomorphic maps
• Integrability conditions
• Coverings of Lie groupoids
• Connected smooth manifold
• Universal coverings
• Covering spaces