Abstract. In this note we calculate Gromov symplectic width and HoferZehnder symplectic capacity for the classical domains.Mathematics Subject Classification: 53D35, 57R17, 53D05

No abstract

No abstract

Orbifold is a generalization of manifold. There are three definitions of the orbifold Euler characteristic: the alternating sum of inverses of the orders of isotropy subgroups of simplices, the alternating sum of the indices of some vector field at its isolated singularities, and the alternating sum of multiplicities of some transversal multisection at its regular zero points. Satake has shown that the first two numbers are equal. In this note, we prove that the latter two are also equal, and this result is verified in the case of n-teardrop.Mathematics Subject Classification (2010). 57R18, 53D99.

Given a basic closed 1‐form on a Lie groupoid scriptG, the Morse–Novikov cohomology groups Hθnfalse(scriptGfalse) are defined in this paper. They coincide with the usual de Rham cohomology groups HdRnfalse(scriptGfalse) when θ is exact and with the usual Morse–Novikov cohomology groups Hθnfalse(Mfalse) when scriptG is the unit groupoid M⇉M generated by a smooth manifold M. We prove that the Morse–Novikov cohomology groups are invariant under Morita equivalences of Lie groupoids. On orbifold groupoids, we show that these groups are isomorphic to sheaf cohomology groups. Finally, when θ is not exact, we extend a vanishing theorem from smooth manifolds to orbifold groupoids.