27 citations · 65 across the 22 of their papers we have counts for
7 papers · 1 filter
Cyclic group actions and embedded spheres in 4-manifolds
M. J. D. Hamilton
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-connect…
Homology classes of negative square and embedded surfaces in 4-manifolds
M. J. D. Hamilton
Let X be a simply-connected closed oriented 4-manifold and A an embedded surface of genus g and negative self-intersection -N. We show that for fixed genus g there is an upper boun…
The closure of the symplectic cone of elliptic surfaces
M. J. D. Hamilton
The symplectic cone of a closed oriented 4-manifold is the set of cohomology classes represented by symplectic forms. A well-known conjecture describes this cone for every minimal…
Iterated fibre sums of algebraic Lefschetz fibrations
M. J. D. Hamilton
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 co…
The minimal genus problem for elliptic surfaces
M. J. D. Hamilton
We solve a certain case of the minimal genus problem for embedded surfaces in elliptic 4-manifolds. The proofs involve a restricted transitivity property of the action of the orien…
Representing homology classes by symplectic surfaces
M. J. D. Hamilton
We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.