We give characterizations of contractible curves on proper normal algebraic surfaces in terms of complementary Weil divisors. From this we obtain some generalizations of the classical criteria for contractibility of Castelnuovo and Artin. Furthermore, we will derive a finiteness result on homogeneous spectra defined by Weil divisors on proper normal algebraic surfaces.

For a closed symplectic manifold (M,ω), a compatible almost complex structure J , a 1-periodic time dependent symplectic vector field Z and a homotopy class of closed curves γ we define a Floer complex based on 1-periodic trajectories of Z in the homotopy class γ. We show how to associate to the above data an invariant, the symplectic torsion, which is an element in the Whitehead group Wh(Λ0), ...

The first two authors showed in~\cite{AM1} how the Conley-Zehnder index of any contractible periodic Reeb orbit a non-degenerate toric contact form on good manifold with zero Chern class, i.e. Gorenstein manifold, can be explicitly computed using moment map data. In this paper we show that same explicit method used to compute indices non-contractible orbits. Under appropriate conditions, (finit...