Search results for "Connected sum"

On the signature of four-manifolds with universal covering spin

1993

In this note we study closed oriented 4-manifolds whose universal covering is spin and ask whether there are restrictions on the divisibility of the signature. Since any natural number appears as the signature of a connected sum of r 2,s, without the assumption on the universal covering there cannot exist any restrictions. Certainly, the most famous such restriction was proved by Rohlin in [10], where he showed that the signature a of a smooth 4-dimensional spin manifold is divisible by 16 (compare part (2) of our Main Theorem for a new proof). The Kummer surface K shows that this is the best possible general result. Dividing by a certain free holomorphic involution on K, one obtains the En…

Star calculus on Jacobi manifolds

2002

Abstract We study the Gerstenhaber bracket on differential forms induced by the two main examples of Jacobi manifolds: contact manifolds and l.c.s. manifolds. Moreover, we obtain explicit expressions of the generating operators and the derivations on the algebra of multivector fields. We define star operators for contact manifolds and l.c.s. manifolds and we study some of its properties.

Complex powers on noncompact manifolds and manifolds with singularities

1988

Bridges, channels and Arnold's invariants for generic plane curves

2002

Abstract We define sums of plane curves that generalize the idea of connected sum and show how Arnol'd's invariants behave with respect to them. We also consider the inverse process of decomposition of a curve and as an application, obtain a new method that reduces considerably the amounts of computation involved in the calculation of Arnold's invariants.