Related papers: Spectral Torsion
We construct spectral triples for the C^*-algebra of continuous functions on the quantum SU(2) group and the quantum sphere. There has been various approaches towards building a calculus on quantum spaces, but there seems to be very few…
We consider the Topological String/Spectral theory duality on toric Calabi-Yau threefolds obtained from the resolution of the cone over the $Y^{N,0}$ singularity. Assuming Kyiv formula, we demonstrate this duality in a special regime thanks…
We prove a spectral upper bound for the torsion function of symmetric stable processes that holds for convex domains in $\mathbb{R}^d$. Our bound is explicit and captures the correct order of growth in $d$, improving upon the existing…
We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the dressed scalar…
As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete…
This paper mainly focuses on the CR analogue of the three-circle theorem in a complete noncompact pseudohermitian manifold of vanishing torsion being odd dimensional counterpart of K\"ahler geometry. In this paper, we show that the CR…
We prove that if an integer homology three-sphere contains an embedded incompressible torus, then its fundamental group admits irreducible SU(2)-representations. Our methods use instanton Floer homology, and in particular the surgery exact…
We introduce a class of one-ended open 3-manifolds which can be `recursively' defined from two compact 3-manifolds, and construct examples of manifolds in this class which fail to have a toric decomposition in the sense of Jaco-Shalen and…
We present the quantum mechanics of "partial-trace" non-linear sigma models, on the grounds of a fully symmetry-based procedure. After the general scheme is sketched, the particular example of a particle on the two-sphere is explicitly…
We consider deformations of the scalar curvature of a partially integrable pseudohermitian manifold, in analogy with the work of Fischer and Marsden on Riemannian manifolds. In particular, we introduce and discuss $R$-singular spaces, give…
We construct a spectral triple on a quantum Heisenberg manifold, which generalizes the results of Chakraborty and Shinha, and associate to it an energy functional on the set of projections, following the approach of Mathai-Rosenberg to…
We refine the reconstruction theorem for almost-commutative spectral triples to a result for real almost-commutative spectral triples, clarifying, in the process, both concrete and abstract definitions of real commutative and…
Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads…
We exhibit large classes of examples of noncommutative finite-dimensional manifolds which are (non-formal) deformations of classical manifolds. The main result of this paper is a complete description of noncommutative three-dimensional…
We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth compact manifolds. The algebra, which is assumed to be…
In this article, we investigate deformation problems of $Q$-curvature on closed Riemannian manifolds. One of the most crucial notions we use is the $Q$-singular space, which was introduced by Chang-Gursky-Yang during 1990's. Inspired by the…
We consider the interpretation in classical geometry of conformal field theories constructed from orbifolds with discrete torsion. In examples we can analyze, these spacetimes contain ``stringy regions'' that from a classical point of view…
The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational molecular spectra is explicitly proved and a connection of this Hamiltonian to the formalism of Amal'sky is…
Spectrum is an important numerical invariant of an isolated hypersurface singularity, connecting its topological and analytic structures. The well-known Hertling conjecture tells the relation of range and variance of exponents i.e. elements…
We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…