Critical Values of Moment Maps on Quantizable Manifolds

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Tetraplectic Structures, Tri-moment Maps, and Quaternionic Flag Manifolds

The purpose of this note is to define a tri-moment map for certain manifolds with an Sp(1)-action. We show how this map can be used ro reduce such manifolds. The images of such maps for quaternionic flag manifolds, which are defined using the Dieudonné determinant, resemble the polytopes from the complex case.

Fusion of Symmetric D-branes and Verlinde Rings

We explain how multiplicative bundle gerbes over a compact, connected and simple Lie group G lead to a certain fusion category of equivariant bundle gerbe modules given by pre-quantizable Hamiltonian LG-manifolds arising from Alekseev-Malkin-Meinrenken’s quasiHamiltonian G-spaces. The motivation comes from string theory namely, by generalising the notion of D-branes in G to allow subsets of G t...

Dirac structures, moment maps and quasi-Poisson manifolds

We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian quasi-Poisson manifolds fit into this framework by constructing an “inversion” procedure relating quasi-Poisson bivectors to twisted Dirac structures. Dedicated to Al...

Moment Maps and Non-compact Cobordisms

We define a moment map for a torus action on a smooth manifold without a two-form. Cobordisms of such structures are meaningful even if the manifolds are non compact, as long as the moment maps are proper. We prove that a compact manifold with a torus action and a moment map is cobordant the normal bundle of its fixed point set. Two formulas follow easily: Guillemin’s topological version of the...