10 papers
Morse field theory
Ralph L. Cohen, Paul Norbury
In this paper we define and study the moduli space of metric-graph-flows in a manifold M. This is a space of smooth maps from a finite graph to M, which, when restricted to each ed…
Closed geodesics on incomplete surfaces
Paul Norbury, J. Hyam Rubinstein
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening meth…
Minimal spheres of arbitrarily high Morse index
Joel Hass, Paul Norbury, J. Hyam Rubinstein
We construct a smooth Riemannian metric on any 3-manifold with the property that there are genus zero embedded minimal surfaces of arbitrarily high Morse index.
Hyperbolic monopoles and holomorphic spheres
Michael K. Murray, Paul Norbury, Michael A. Singer
We associate to an SU(2) hyperbolic monopole a holomorphic sphere embedded in projective space and use this to uncover various features of the monopole.
The Orevkov invariant of an affine plane curve
Walter D. Neumann, Paul Norbury
We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the…
Boundary algebras of hyperbolic monopoles
Paul Norbury
We prove the conjecture that a monopole in three-dimensional anti-de Sitter space can be completely determined by its ``holographic'' image on the conformal boundary two-sphere.