9 citations · 30 across the 21 of their papers we have counts for
12 papers · 1 filter
Slices for reductive group actions in algebraic and holomorphic symplectic geometry
Peter Crooks, Rebecca Goldin, Yiannis Loizides
Symplectic slice theorems elucidate the local structure of symplectic manifolds carrying Hamiltonian actions of compact Lie groups. We generalize these theorems in two natural sett…
Families of elliptic boundary problems and index theory of the Atiyah-Bott classes
Yiannis Loizides
We study a natural family of non-local elliptic boundary problems on a compact oriented surface parametrized by the moduli space of flat -connections with fr…
Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We extend the Marsden-Weinstein reduction theorem and the Darboux-Moser-Weinstein theorem to symplectic Lie algebroids. We also obtain a coisotropic embedding theorem for symplecti…
Riemannian foliations and geometric quantization
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-…
Index formula for Hamiltonian loop group spaces
Yiannis Loizides
We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to…
Log symplectic manifolds and
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We show, under an orientation hypothesis, that a log symplectic manifold with simple normal crossing singularities has a stable almost complex structure, and hence is Spin. In…
Geometric quantization of b-symplectic manifolds
Maxim Braverman, Yiannis Loizides, Yanli Song
We introduce a method of geometric quantization for compact -symplectic manifolds in terms of the index of an Atiyah-Patodi-Singer (APS) boundary value problem. We show further…
Quasi-polynomials and the singular theorem
Yiannis Loizides
In this short note we revisit the `shift-desingularization' version of the theorem for possibly singular symplectic quotients. We take as starting point an elegant proof…
Norm-square localization and the quantization of Hamiltonian loop group spaces
Yiannis Loizides, Yanli Song
In an earlier article we introduced a new definition for the `quantization' of a Hamiltonian loop group space , involving the equivariant -index of a Dirac-type o…
The decomposition formula for Verlinde Sums
Yiannis Loizides, Eckhard Meinrenken
We prove a decomposition formula for Verlinde sums (rational trigonometric sums), as a discrete counterpart to the Boysal-Vergne decomposition formula for Bernoulli series. Motivat…
Spinor modules for Hamiltonian loop group spaces
Yiannis Loizides, Eckhard Meinrenken, Yanli Song
Let be the loop group of a compact, connected Lie group . We show that the tangent bundle of any proper Hamiltonian -space has a natural completion $\over…
Norm-square localization for Hamiltonian -spaces
Yiannis Loizides
We prove a formula for twisted Duistermaat-Heckman distributions associated to a Hamiltonian -space. The terms of the formula are localized at the critical points of the norm-s…