14 citations · 70 across the 24 of their papers we have counts for
10 papers · 1 filter
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-…
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…
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…
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…
On the Vergne conjecture
Peter Hochs, Yanli Song
Consider a Hamiltonian action by a compact Lie group on a possibly noncompact symplectic manifold. We give a short proof of a geometric formula for decomposition into irreducible r…
Dirac operators on quasi-Hamiltonian G-spaces
Yanli Song
We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with i…
A K-homological approach to the quantization commutes with reduction problem
Yanli Song
Kasparov defined a distinguished K-homology fundamental class, so called the Dirac element. We prove a localization formula for the Dirac element in K-homology of crossed product o…
Proper maps, bordism, and geometric quantization
Yanli Song
Let be a compact connected Lie group acting on a stable complex manifold with equivariant vector bundle . Besides, suppose is an equivariant map from to the Lie…