Related papers: On the Vergne conjecture
We establish an S^1-equivariant index theorem for Dirac operators on Z/k-manifolds. As an application, we generalize the Atiyah-Hirzebruch vanishing theorem for S^1-actions on closed spin manifolds to the case of Z/k-manifolds.
In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants…
Let G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifold M, with compact quotient. There is an assembly map which associates to any G-equivariant K-homology class on M, an element of the…
We prove the following conjecture by S. Carpentier, A. De Sole, and V. G. Kac: Let K be a differential field and R be a differential subring of K. Let M be a matrix whose elements are differential operators with coefficents in R. Then, if M…
Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ via symplectic reduction. If $M$ is also a symplectic groupoid, then its multiplication…
In this thesis, we investigate the proof of the Baum-Connes Conjecture with Coefficients for a-$T$-menable groups. We will mostly and essentially follow the argument employed by N. Higson and G. Kasparov in the paper [Nigel Higson and…
The Lie algebra generated by $m\ $ $p$-dimensional Grassmannian Dirac operators and $m\ $ $p$-dimensional vector variables is identified as the orthogonal Lie algebra $\mathfrak{so}(2m+1)$. In this paper, we study the space $\mathcal{P}$ of…
In this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator.
We prove a decomposition formula for Verlinde sums (rational trigonometric sums), as a discrete counterpart to the Boysal-Vergne decomposition formula for Bernoulli series. Motivated by applications to fixed point formulas in Hamiltonian…
In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
The unitary dual of $GL(n, \mathbb{R})$ was classified by Vogan in the 1980s. Focusing on the irreducible unitary representations of $GL(n, \mathbb{R})$ with half-integral infinitesimal characters, we find that Speh representations and the…
The authors of that work [Phys. Rev. D 88, 084014 (2013)], arXiv:1308.4552, derive quantum-mechanical equations valid for the covariant Dirac equation by restricting the choice of the tetrad field through the use of the "Schwinger gauge".…
We prove Zimmer's conjecture for $C^2$ actions by finite-index subgroups of $\mathrm{SL}(m,\mathbb{Z})$ provided $m>3$. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in…
The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…
We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between…
We prove the $K$-theoretic Farrell-Jones conjecture for groups as in the title with coefficient rings and $C^*$-algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes…
For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra ${\mathfrak g}^*$ by the…
Denote by $M(P)$ the configuration space of a planar polygonal linkage, that is, the space of all possible planar configurations modulo congruences, including configurations with self-intersections. A particular interest attracts its subset…
M. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kaehler manifold preserved by the complexification of the Hamiltonian group action. V. Guillemin and R. Sjamaar generalized this…