• Publications
  • Influence
Geometric quantization and families of inner products
Abstract We formulate a quantization commutes with reduction principle in the setting where the Lie group G, the symplectic manifold it acts on, and the orbit space of the action may all beExpand
  • 28
  • 3
  • PDF
Quantisation commutes with reduction at discrete series representations of semisimple groups
Abstract Using the analytic assembly map that appears in the Baum–Connes conjecture in noncommutative geometry, we generalise the Guillemin–Sternberg conjecture that ‘quantisation commutes withExpand
  • 25
  • 2
  • PDF
An equivariant Atiyah-Patodi-Singer index theorem for proper actions
Consider a proper, isometric action by a unimodular locally compact group $G$ on a Riemannian manifold $M$ with boundary, such that $M/G$ is compact. Then an equivariant Dirac type operator on $M$Expand
  • 5
  • 1
  • PDF
Equivariant indices of Spin$^c$-Dirac operators for proper moment maps
We define an equivariant index of Spin$^c$-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the index decomposes intoExpand
  • 19
  • 1
  • PDF
An equivariant index for proper actions II: properties and applications
In the first part of this series, we defined an equivariant index without assuming the group acting or the orbit space of the action to be compact. This allowed us to generalise an index of deformedExpand
  • 6
  • PDF
Quantization, noncommutative geometry, and symmetry
Positive scalar curvature and an equivariant Callias-type index theorem for proper actions
For a proper action by a locally compact group $G$ on a manifold $M$ with a $G$-equivariant Spin-structure, we obtain obstructions to the existence of complete $G$-invariant Riemannian metrics withExpand
  • 1
  • PDF
Coarse geometry and Callias quantisation
Consider a proper, isometric action by a unimodular, locally compact group $G$ on a complete Riemannian manifold $M$. For equivariant elliptic operators that are invertible outside a cocompact subsetExpand
  • 4
  • PDF
Equivariant Callias index theory via coarse geometry
The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion ofExpand
  • 4
  • PDF
K T ] 2 0 Fe b 20 19 Equivariant Callias index theory via coarse geometry
The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion ofExpand