40,769 research outputs found
Iterated fibre sums of algebraic Lefschetz fibrations
Let M denote the total space of a Lefschetz fibration, obtained by blowing up
a Lefschetz pencil on an algebraic surface. We consider the n-fold fibre sum
M(n), generalizing the construction of the elliptic surfaces E(n). For a
Lefschetz pencil on a simply-connected minimal surface of general type we
partially calculate the Seiberg-Witten invariants of the fibre sum M(n) using a
formula of Morgan-Szabo-Taubes. As an application we derive an obstruction for
self-diffeomorphisms of the boundary of the tubular neighbourhood of a general
fibre in M(n) to extend over the complement of the neighbourhood. Similar
obstructions are known in the case of elliptic surfaces.Comment: 14 pages; to appear in Quart. J. Mat
Cyclic group actions and embedded spheres in 4-manifolds
In this note we derive an upper bound on the number of 2-spheres in the fixed
point set of a smooth and homologically trivial cyclic group action of prime
order on a simply-connected 4-manifold. This improves the a priori bound which
is given by one half of the Euler characteristic of the 4-manifold. The result
also shows that in some cases the 4-manifold does not admit such actions of a
certain order at all or that any such action has to be pseudofree.Comment: 13 pages; to appear in Proc. Amer. Math. So
Representing homology classes by symplectic surfaces
We derive an obstruction to representing a homology class of a symplectic
4-manifold by an embedded, possibly disconnected, symplectic surface.Comment: 5 page
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