Related papers: Ideal Turaev-Viro invariants
It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the $G$--modules $W$ and $m$ copies of $V$ can be separated by polynomial…
We study the Turaev-Viro invariant as the Euclidean Chern-Simons-Witten gravity partition function with positive cosmological constant. After explaining why it can be identified as the partition function of 3-dimensional gravity, we show…
We construct an invariant of 3-manifolds using a modification of the Kontsevich integral and Kirby's calculus. This invariant, as expected in perturbative Chern-Simon theory, takes values in the algebra of oriented 3-valent graphs. This…
We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for…
Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
In the prequel of this paper, Kauffman and Ogasa introduced new topological quantum invariants of compact oriented 3-manifolds with boundary where the boundary is a disjoint union of two identical surfaces. The invariants are constructed…
A new topological invariant of closed connected orientable four-dimensional manifolds is proposed. The invariant, constructed via surgery on a special link, is a four-dimensional counterpart of the celebrated SU(2) three-manifold invariant…
Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.
We prove that the Witten-Reshetikhin-Turaev (WRT) SO(3) invariant of an arbitrary 3-manifold M is always an algebraic integer. Moreover, we give a rational surgery formula for the unified invariant dominating WRT SO(3) invariants of…
Vassiliev's knot invariants can be computed in different ways but many of them as Kontsevich integral are very difficult. We consider more visual diagram formulas of the type Polyak-Viro and give new diagram formula for the two basic…
The main theorem describes the behaviour of the stable cohomotopy invariant defined in the first article (joint with M. Furuta) in this series of two under the operation of taking connected sums of four-manifolds: The invariant of a…
We prove the Turaev-Viro invariants volume conjecture for a "universal" class of cusped hyperbolic 3-manifolds that produces all 3-manifolds with empty or toroidal boundary by Dehn filling. This leads to two-sided bounds on the volume of…
The main observation of this note is that the Lebesgue measure $\mu$ in the Tur\'an-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant $\omega \ge \mu$, which can be effectively estimated in…
We investigate the conjectural relations between the Reshetikhin-Turaev-Witten quantum SU(2) invariants and the volume of hyperbolic 3-manifolds. Given a finite set of sufficiently large positive integers, say J, we construct examples of…
We introduce a triple coproduct for knots on surfaces, providing a commutative framework that decomposes a single-component diagram into three components (Section 2). This construction is motivated by the interplay between intersection…
We develop an iterative technique for computing the unstable and stable eigenfunctions of the invariant tori of diffeomorphisms. Using the approach of Jorba, the linearized equations are rewritten as a generalized eigenvalue problem.…
We consider the problem of minimizing variational integrals defined on \cc{nonlinear} Sobolev spaces of competitors taking values into the sphere. The main novelty is that the underlying energy features a non-uniformly elliptic integrand…
Given a family $\varphi= (\varphi_1, \ldots, \varphi_d)\in \mathbb{Z}[T]^d$ of $d$ distinct nonconstant polynomials, a positive integer $k\le d$ and a real positive parameter $\rho$, we consider the mean value $$ M_{k, \rho} (\varphi, N) =…
We introduce and study equivariant Hilbert series of ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the monoid $Inc(\mathbb{N})$ of strictly increasing functions.…