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- Michael Usher
- 2006

Let X_1, X_2 be symplectic 4-manifolds containing symplectic surfaces F_1,F_2 of identical positive genus and opposite squares. Let Z denote the symplectic sum of X_1 and X_2 along the F_k. Using… (More)

- Michael Usher, Jun Zhang
- 2016

We construct "barcodes" for the chain complexes over Novikov rings that arise in Novikov's Morse theory for closed one-forms and in Floer theory on not-necessarily-monotone symplectic manifolds. In… (More)

- Michael Usher
- 2011

We show that if (M ,ω) is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer’s metric on the group of… (More)

- Michael Usher
- 2008

The chain complexes underlying Floer homology theories typically carry a real-valued filtration, allowing one to associate to each Floer homology class a spectral number defined as the infimum of the… (More)

- Michael Usher
- 2004

Simon Donaldson and Ivan Smith recently studied symplectic surfaces in symplectic 4{manifolds X by introducing an invariant DS associated to any Lefschetz bration on blowups of X which counts… (More)

- Michael Usher
- 2007

Modulo trivial exceptions, we show that symplectic sums of symplectic 4-manifolds along surfaces of positive genus are never rational or ruled, and we enumerate each case in which they have Kodaira… (More)

- Michael Usher
- 2008

Using the Oh-Schwarz spectral invariants and some arguments of Frauenfelder, Ginzburg, and Schlenk, we show that the \pi_1-sensitive Hofer-Zehnder capacity of any subset of a closed symplectic… (More)

We consider various constructions of monotone Lagrangian submanifolds of $C P^n, S^2\times S^2$, and quadric hypersurfaces of $C P^n$. In $S^2\times S^2$ and $C P^2$ we show that several different… (More)

- Megan A Kelly, Michael Usher, Beata Ujvari, Thomas Madsen, A. J. Hulbert
- Mechanisms of Ageing and Development
- 2014

The membrane pacemaker theory of ageing proposes that the polyunsaturated fatty acid (PUFA) composition of membrane lipids of a species is an important determinant of its maximum lifespan. We report… (More)

- Michael Usher
- 2006

Adapting a construction of D Salamon involving the U(1) vortex equations, we explore the properties of a Floer theory for 3-manifolds that fiber over S^1 which exhibits several parallels with… (More)