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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 be… Expand

28 3- PDF

Quantisation commutes with reduction at discrete series representations of semisimple groups

- P. Hochs
- Mathematics
- 21 May 2007

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 with… Expand

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 into… Expand

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 deformed… Expand

6- PDF

Quantization, noncommutative geometry, and symmetry

- G. Heckman, N. P. Landsman, +5 authors N. Kowalzig
- Physics
- 1 September 2002

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 with… Expand

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 subset… Expand

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 of… Expand

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 of… Expand