Related papers: The simplest Exotic Invariant (E3)
An expository account of Ribet's modular construction
In this short paper, we survey the results on commutative automorphic loops and give a new construction method. Using this method, we present new classes of commutative automorphic loops of exponent 2 with trivial center.
By using an approach of the invariant theory we obtain a new formula for the ordinary generating function of the numbers of the simple graphs with $n$ nodes.
We compute the cohomological invariants with coefficients in $\mathbb{Z}/p\mathbb{Z}$ of the stack $\mathscr{H}_3$ of hyperelliptic curves of genus $3$ over an algebraically closed field.
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.
In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.
This is the third paper in a series devoted to enumerating the prime alternating knots and links. This paper establishes a method for enumerating the prime alternating links. It is shown that one may choose any prime alternating link…
We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…
We derive a formula for the Dijkgraaf-Witten invariants of orientable Seifert 3-manifolds with orientable bases.
We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.
A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot - or, in some cases, only -- periodic solutions. Several examples (ODEs and PDEs) are exhibited.
We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
We provide a way to produce knots in $S^3$ from signed chord diagrams, and prove that every knot can be produced in this way. Using these diagrams, we generalize the fundamental theorem of finite type invariants. We also provide moves for…
In this paper give a survey about L^2-invariants focusing on 3-manifolds.
A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for…
We describe a simple way of constructing torus fibrations $T^3\to X\to S^3$ which degenerate canonically over a knot or link in $S^3$. We show that the topological invariants of $X$ can be computed algebraically from the monodromy…
The aim of this article is to show the existence, and also give an explicit construction, of infinite sets of orthogonal exponentials for certain families of convex polytopes which include simple-rational polytopes and also non simple…