This article establishes the algebraic covering theory of quandles. For every connected quandle Q with base point q ∈ Q, we explicitly construct a universal covering p: (Q̃,q̃̃) → (Q,q). This in turn leads us to define the algebraic fundamental group $\pi ₁(Q,q):=Aut\left(p\right)=g\in Adj{\left(Q\right)}^{\text{'}}|q^g=q$, where Adj(Q) is the adjoint group of Q. We then establish the Galois correspondence between connected coverings of (Q,q) and subgroups of π₁(Q,q). Quandle coverings are thus formally analogous to coverings of topological spaces, and resemble Kervaire’s...

We propose a direction of study of nonabelian theta functions by establishing an analogy between the Weyl quantization of a one-dimensional particle and the metaplectic representation on the one hand, and the quantization of the moduli space of flat connections on a surface and the representation of the mapping class group on the space of nonabelian theta functions on the other. We exemplify this with the cases of classical theta functions and of the nonabelian theta functions for the gauge group...

This is a survey (including new results) of relations ?some emergent, others established? among three notions which the 1980s saw introduced into knot theory: quasipositivity of a link, the enhanced Milnor number of a fibered link, and the new link polynomials. The Seifert form fails to determine these invariants; perhaps there exists an ?enhanced Seifert form? which does.

Soit $\phi :=(f,g):{ℂ}^2\to {ℂ}^2$ où $f$ et $g$ sont des applications polynomiales. Nous établissons le lien qui existe entre le polygone de Newton de la courbe réunion du discriminant et du lieu de non-propreté de $\phi$ et la topologie des entrelacs à l’infini des courbes affines $f^{-1}\left(0\right)$ et $g^{-1}\left(0\right)$. Nous en déduisons alors des conséquences liées à la conjecture du jacobien.