Hessel Posthuma
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View article: Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills theory
Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills theory Open
In Yang-Mills gauge theory on a Euclidean Cauchy surface the group of physical gauge symmetries carrying direct empirical significance is often believed to be $\mathcal{G}_\text{DES}=\mathcal{G}^I/\mathcal{G}^\infty_0$, where $\mathcal{G}^…
View article: Hochschild cohomology of Lie-Rinehart algebras
Hochschild cohomology of Lie-Rinehart algebras Open
We compute the Hochschild cohomology of universal enveloping algebras of Lie-Rinehart algebras in terms of the Poisson cohomology of the associated graded quotient algebras. Central in our approach are two cochain complexes of "nonlinear C…
View article: Lie groupoid deformations and convolution algebras
Lie groupoid deformations and convolution algebras Open
We define a morphism from the deformation complex of a Lie groupoid to the Hochschild complex of its convolution algebra, and show that it maps the class of a geometric deformation to the algebraic class of the induced deformation in Hochs…
View article: Delocalized eta invariants of the signature operator on G-proper manifolds
Delocalized eta invariants of the signature operator on G-proper manifolds Open
Let $G$ be a connected, linear real reductive group and let $X$ be a cocompact $G$-proper manifold without boundary. We define delocalized eta invariants associated to a $L^2$-invertible perturbed Dirac operator $D_X+A$ with $A$ a suitable…
View article: A note on the equivariant Chern character in Noncommutative Geometry
A note on the equivariant Chern character in Noncommutative Geometry Open
Given a smooth action of a Lie group on a manifold, we give two constructions of the Chern character of an equivariant vector bundle in the cyclic cohomology of the crossed product algebra. The first construction associates a cycle to the …
View article: On the Hochschild homology of proper Lie groupoids
On the Hochschild homology of proper Lie groupoids Open
We study the Hochschild homology of the convolution algebra of a proper Lie groupoid by introducing a convolution sheaf over the space of orbits. We develop a localization result for the associated Hochschild homology sheaf, and we prove t…
View article: Higher orbital integrals, rho numbers and index theory
Higher orbital integrals, rho numbers and index theory Open
Let $G$ be a connected, linear real reductive group. We give sufficient conditions ensuring the well-definedness of the delocalized eta invariant $η_g (D_X)$ associated to a Dirac operator $D_X$ on a cocompact $G$-proper manifold $X$ and t…
View article: Lie Groupoid Deformations and Convolution Algebras
Lie Groupoid Deformations and Convolution Algebras Open
We define a morphism from the deformation complex of a Lie groupoid to the Hochschild complex of its convolution algebra, and show that it maps the class of a geometric deformation to the algebraic class of the induced deformation in Hochs…
View article: Higher genera for proper actions of Lie groups, Part 2: the case of manifolds with boundary
Higher genera for proper actions of Lie groups, Part 2: the case of manifolds with boundary Open
Let G be a finitely connected Lie group and let K be a maximal compact subgroup. Let M be a cocompact G-proper manifold with boundary, endowed with a G-invariant metric which is of product type near the boundary. Under additional assumptio…
View article: On the Hochschild homology of convolution algebras of proper Lie groupoids
On the Hochschild homology of convolution algebras of proper Lie groupoids Open
We study the Hochschild homology of the convolution algebra of a proper Lie groupoid by introducing a convolution sheaf over the space of orbits. We develop a localization result for the associated Hochschild homology sheaf, and prove that…
View article: Resolutions of Proper Riemannian Lie Groupoids
Resolutions of Proper Riemannian Lie Groupoids Open
In this paper we prove that every proper Lie groupoid admits a regularization to a regular proper Lie groupoid. When equipped with a Riemannian metric, we show that it admits regularization to a regular Riemannian proper Lie groupoid, arbi…
View article: Classification of crystalline topological insulators through K-theory
Classification of crystalline topological insulators through K-theory Open
Topological phases for free fermions in systems with crystal symmetry are classified by the topology of the valence band viewed as a vector bundle over the Brillouin zone. Additional symmetries, such as crystal symmetries which act non-tri…
View article: Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed
Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed Open
We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure…
View article: The Grauert--Grothendieck complex on differentiable spaces and a sheaf complex of Brylinski
The Grauert--Grothendieck complex on differentiable spaces and a sheaf complex of Brylinski Open
We use the Grauert--Grothendieck complex on differentiable spaces to study basic relative forms on the inertia space of a compact Lie group action on a manifold. We prove that the sheaf complex of basic relative forms on the inertia space …
View article: The bi-Hamiltonian cohomology of a scalar Poisson pencil
The bi-Hamiltonian cohomology of a scalar Poisson pencil Open
We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless\nPoisson pencil in a single dependent variable using a spectral sequence method.\nAs in the KdV case, we obtain that $BH^p_d(\\hat{F}, d_1,d_2)$ is isomorphic to\n$\\m…
View article: An index theorem for Lie algebroids
An index theorem for Lie algebroids Open
We study Lie algebroids from the point of view noncommutative geometry. More specifically, using ideas from deformation quantization, we use the PBW-theorem for Lie algebroids to construct a Fedosov-type resolution for the associated sheav…
View article: Quantization of Whitney functions and reduction
Quantization of Whitney functions and reduction Open
For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is…