31 citations · 151 across the 36 of their papers we have counts for
40 papers
Well-tempered symmetric spaces
Alexandre Afgoustidis, Peter Hochs, Shintaro Nishikawa +1
Let be a real reductive symmetric space. We consider the support of the Plancherel measure for the regular representation of on , and its Fell topology. We firs…
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…
A higher index and rapidly decaying kernels
Hao Guo, Peter Hochs, Hang Wang
We construct an index of first-order, self-adjoint, elliptic differential operators in the -theory of a Fréchet algebra of smooth kernels with faster than exponential off-diagon…
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 higher index on finite-volume locally symmetric spaces
Hao Guo, Peter Hochs, Hang Wang
Let be a connected, real semisimple Lie group. Let be maximal compact, and let be discrete and such that has finite volume. If the real rank of …
Equivariant Spectral Flow for Families of Dirac-type Operators
Peter Hochs, Aquerman Yanes
In the setting of a proper, cocompact action by a locally compact, unimodular group on a Riemannian manifold, we construct equivariant spectral flow of paths of Dirac-type oper…
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 equivariant Atiyah-Patodi-Singer index theorem for proper actions II: the -theoretic index
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. Then an equivariant Dirac-type…
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…
An equivariant orbifold index for proper actions
Peter Hochs, Hang Wang
For a proper, cocompact action by a locally compact group of the form , with compact, we define an -equivariant index of -transversally elliptic oper…
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…
Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions
Peter Hochs, A. J. Roberts
We prove that a general class of nonlinear, non-autonomous ODEs in Fréchet spaces are close to ODEs in a specific normal form, where closeness means that solutions of the normal fo…
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…
Equivariant Callias index theory via coarse geometry
Hao Guo, Peter Hochs, Varghese Mathai
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 s…
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…
Orbital integrals and -theory classes
Peter Hochs, Hang Wang
Let be a semisimple Lie group with discrete series. We use maps defined by orbital integrals to recover group theoretic information about , inclu…
Shelstad's character identity from the point of view of index theory
Peter Hochs, Hang Wang
Shelstad's character identity is an equality between sums of characters of tempered representations in corresponding -packets of two real, semisimple, linear, algebraic groups t…