相关论文: Noncommutative residue invariants for CR and conta…

We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.

We use contact geometry to describe the monoid of projectively equivariant meromorphic differential operators on a complex curve, quantization of which generalizes known constructions of classical equivariants to non-commutative function…

Oeljeklaus-Toma (OT) manifolds are complex non-K\"ahler manifolds whose construction arises from specific number fields. In this note, we compute their de Rham cohomology in terms of invariants associated to the background number field.…

In this article we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson-fermion correspondence, the analytic torsion, the Chern-Simons and $\eta$ invariants, as well as the generation function…

Using the associativity relations of the topological Sigma Models with target spaces, $CP^3, CP^4$ and $Gr(2,4)$ , we derive recursion relations of their correlation and evaluate them up to certain order in the expansion over the…

We introduce a new invariant, the \textit{positive idempotent group}, for strongly asymptotically dynamically convex contact manifolds. This invariant can be used to distinguish different contact structures. As an application, for any…

Given a transverse link in the standard contact 3-sphere, we study the contact manifold that arises as a branched double cover of the sphere. We give a contact surgery description of such manifolds, which allows to determine the Heegaard…

Given any unoriented link diagram, a group of new knot invariants are constructed. Each of them satisfies a generalized 4 term skein relation. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations…

We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its…

We study the existence problem for complete contact forms with constant Tanaka--Webster scalar curvature on non-compact strictly pseudoconvex CR manifolds. We prove that, under mild assumptions, the universal cover of a compact strictly…

We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields $h:=\frac{1}{2}\pounds _\xi \varphi$ and $\ell := R(\cdot,\xi)\xi$, emphasizing analogies and differences with respect to the contact metric case.…

The notion of non-projectible contact forms on a given compact manifold $M$ is introduced by the first-named author in [Ohb], the set of which he also shows is a residual subset of the set of (coorientable) contact forms, both in the case…

We study a CR analogue of the Ahlfors derivative for conformal immersions of Stowe [23] that generalizes the CR Schwarzian derivative studied earlier by the second-named author [21]. This notion possesses several important properties…

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. Such model can…

We state and prove a topological recursion relation that expresses any genus-g Gromov-Witten invariant of a projective manifold with at least a (3g-1)-st power of a cotangent line class in terms of invariants with fewer cotangent line…

We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c manifolds; and conversely, in the presence…

We study the action of the group of contact diffeomorphisms on CR deformations of compact three-dimensional CR manifolds. Using anisotropic function spaces and an anisotropic structure on the space of contact diffeomorphisms, we establish…

Let $\gp$ be a finite group acting on a compact manifold $M$ and $\maA(M)$ denote the algebra of classical complete symbols on $M$. We determine all traces on the cross-product algebra $\maA(M) \rtimes \Gamma$. These traces appear as…

In this paper we construct a topological model for the Witten-Reshetikhin-Turaev invariants for $3$-manifolds coming from the quantum group $U_q(sl(2))$, as graded intersection pairings of homology classes in configuration spaces. More…

The Chern-Simons invariants of irreducible U(n)- flat connections on compact hyperbolic 3-manifolds of the form {\Gamma}\H^3 are derived. The explicit formula for the Chern-Simons functional is given in terms of Selberg type zeta functions…