28 research outputs found
Inequivalent contact structures on Boothby-Wang 5-manifolds
We consider contact structures on simply-connected 5-manifolds which arise as
circle bundles over simply-connected symplectic 4-manifolds and show that
invariants from contact homology are related to the divisibility of the
canonical class of the symplectic structure. As an application we find new
examples of inequivalent contact structures in the same equivalence class of
almost contact structures with non-zero first Chern class.Comment: 27 pages; to appear in Math. Zeitschrif
Magnetic Domains
Recently a Nahm transform has been discovered for magnetic bags, which are
conjectured to arise in the large n limit of magnetic monopoles with charge n.
We interpret these ideas using string theory and present some partial proofs of
this conjecture. We then extend the notion of bags and their Nahm transform to
higher gauge theories and arbitrary domains. Bags in four dimensions
conjecturally describe the large n limit of n self-dual strings. We show that
the corresponding Basu-Harvey equation is the large n limit of an equation
describing n M2-branes, and that it has a natural interpretation in loop space.
We also formulate our Nahm equations using strong homotopy Lie algebras.Comment: 42 pages, minor improvements, published versio