67 citations · 204 across the 35 of their papers we have counts for
9 papers · 1 filter
Higher genera for proper actions of Lie groups, Part 2: the case of manifolds with boundary
Paolo Piazza, Hessel Posthuma
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…
On the Hochschild homology of convolution algebras of proper Lie groupoids
Markus J. Pflaum, Hessel B. Posthuma, Xiang Tang
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 f…
Higher genera for proper actions of Lie groups
Paolo Piazza, Hessel Posthuma
Let G be a Lie group with finitely many connected components and let K be a maximal compact subgroup. We assume that G satisfies the rapid decay (RD) property and that G/K has non-…
The localized longitudinal index theorem for Lie groupoids and the van Est map
M. J. Pflaum, H. Posthuma, X. Tang
We define the "localized index" of longitudinal elliptic operators on Lie groupoids associated to Lie algebroid cohomology classes. We derive a topological expression for these num…
The cyclic theory of Hopf algebroids
Niels Kowalzig, Hessel Posthuma
We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory…
Cyclic cocycles on deformation quantizations and higher index theorems
M. Pflaum, H. Posthuma, X. Tang
We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic vector space. Using this cyclic cocycle we construct an explicit, local, quasi-isomorphism from the com…