31 citations · 151 across the 36 of their papers we have counts for
20 papers · 1 filter
Quantitative partitioned index theorem and noncompact band-width
Peter Hochs, Jinmin Wang
Gromov's band-width conjecture gives a precise upper bound for the width of a compact Riemannian band with positive scalar curvature lower bound, assuming that the cross-section of…
A partitioned manifold index theorem for noncompact hypersurfaces
Peter Hochs, Thijs de Kok
Roe's partitioned manifold index theorem applies when a complete Riemannian manifold is cut into two pieces along a compact hypersurface . It states that a version of the in…
The Equivariant Fried Conjecture for Suspension Flow of an Equivariant Isometry
Peter Hochs, Christopher Pirie
The Fried conjecture states that the Ruelle dynamical -function of a flow on a compact maniofold has a well-defined value at , whose absolute value equals the Ray-Singer anal…
An equivariant Guillemin trace formula
Peter Hochs, Hemanth Saratchandran
Guillemin's trace formula is an expression for the distributional trace of an operator defined by pulling back functions along a flow on a compact manifold. We obtain an equivarian…
A Lefschetz fixed-point formula for noncompact fixed-point sets
Peter Hochs
We obtain an equivariant index theorem, or Lefschetz fixed-point formula, for isometries from complete Riemannian manifolds to themselves. The fixed-point set of such an isometry m…
A Ruelle dynamical zeta function for equivariant flows
Peter Hochs, Hemanth Saratchandran
For proper group actions on smooth manifolds, with compact quotients, we define an equivariant version of the Ruelle dynamical -function for equivariant flows satisfying a nonde…
Equivariant analytic torsion for proper actions
Peter Hochs, Hemanth Saratchandran
We construct an equivariant version of Ray-Singer analytic torsion for proper, isometric actions by locally compact groups on Riemannian manifolds, with compact quotients. We obtai…
Spectral Asymmetry and Index Theory on Manifolds with Generalised Hyperbolic Cusps
Peter Hochs, Hang Wang
We consider a complete Riemannian manifold, which consists of a compact interior and one or more -cusps: infinitely long ends of a type that includes cylindrical ends and hyperb…
An absolute version of the Gromov-Lawson relative index theorem
Peter Hochs, Hang Wang
A Dirac operator on a complete manifold is Fredholm if it is invertible outside a compact set. Assuming a compact group to act on all relevant structure, and the manifold to have a…
An index theorem for higher orbital integrals
Peter Hochs, Yanli Song, Xiang Tang
Recently, two of the authors of this paper constructed cyclic cocycles on Harish-Chandra's Schwartz algebra of linear reductive Lie groups that detect all information in the -th…
Positive scalar curvature and an equivariant Callias-type index theorem for proper actions
Hao Guo, Peter Hochs, Varghese Mathai
For a proper action by a locally compact group on a manifold with a -equivariant Spin-structure, we obtain obstructions to the existence of complete -invariant Rieman…
Coarse geometry and Callias quantisation
Hao Guo, Peter Hochs, Varghese Mathai
Consider a proper, isometric action by a unimodular, locally compact group on a complete Riemannian manifold . For equivariant elliptic operators that are invertible outside…
An equivariant Atiyah-Patodi-Singer index theorem for proper actions I: the index formula
Peter Hochs, Bai-Ling Wang, Hang Wang
Consider a proper, isometric action by a unimodular locally compact group on a Riemannian manifold with boundary, such that is compact. For an equivariant, elliptic o…
A geometric formula for multiplicities of -types of tempered representations
Peter Hochs, Yanli Song, Shilin Yu
Let be a connected, linear, real reductive Lie group with compact centre. Let be compact. Under a condition on , which holds in particular if is maximal compact, w…
A fixed point formula and Harish-Chandra's character formula
Peter Hochs, Hang Wang
The main result in this paper is a fixed point formula for equivariant indices of elliptic differential operators, for proper actions by connected semisimple Lie groups on possibly…
Equivariant indices of Spin-Dirac operators for proper moment maps
Peter Hochs, Yanli Song
We define an equivariant index of Spin-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the in…
An equivariant index for proper actions III: the invariant and discrete series indices
Peter Hochs, Yanli Song
We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin-Dirac operators, invariant under actions by po…
Spin-structures and proper group actions
Peter Hochs, Varghese Mathai
We generalise Atiyah and Hirzebruch's vanishing theorem for actions by compact groups on compact Spin-manifolds to possibly noncompact groups acting properly and cocompactly on pos…
Quantising proper actions on Spin-manifolds
Peter Hochs, Varghese Mathai
Paradan and Vergne generalised the quantisation commutes with reduction principle of Guillemin and Sternberg from symplectic to Spin-manifolds. We extend their result to noncom…
Geometric quantization and families of inner products
Peter Hochs, Varghese Mathai
We formulate a quantization commutes with reduction principle in the setting where the Lie group , the symplectic manifold it acts on, and the orbit space of the action may all…