Related papers: Fundamental group in the projective knot theory

This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called flat affine or flat projective Lie groups. Our main results…

Knots naturally appear in continuous dynamical systems as flow periodic trajectories. However, discrete dynamical systems are also closely connected with the theory of knots and links. For example, for Pixton diffeomorphisms, the…

These notes are defining the notion of centric linking system for a locally finite group If a locally finite group $G$ has countable Sylow $p$-subgroups, we prove that, with a countable condition on the set of intersections, the…

Following the Euclidean results of Varopoulos and Pankka--Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold $M$ to admit a nonconstant quasiregular mapping from the sub-Riemannian Heisenberg group…

A rope is a non-singular embedding of a closed interval into R^3, which sends the ends of the interval to some fixed points A and B such that |AB|=1. A rope is short if its length is less than 3. The main result of the paper is that the…

We prove that the Picard group of a connected affine algebraic group $G$ is isomorphic to the fundamental group of the derived subgroup of the reductive algebraic group $G/{\mathscr R}_u(G)$, where ${\mathscr R}_u(G)$ is the unipotent…

Let $f\colon M\to N$ be a proper map between two aspherical compact orientable 3-manifolds with empty or toroidal boundary. We assume that $N$ is not a closed graph-manifold. Suppose that $f$ induces an epimorphism on fundamental groups. We…

Let $X$ be a smooth projective connected curve of genus $g\ge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show…

We extend two results known for aspherical 3-manifolds to $PD_3$-pairs $(P,\partial{P})$ with aspherical ambient space $P$. Every such $PD_3$-pair may be assembled by attaching 1-handles to $PD_3$-pairs with aspherical; ambient space and…

For a commutative ring R with many units, we describe the kernel of H_3(inc): H_3(GL_2(R), Z) --> H_3(GL_3(R), Z). Moreover we show that the elements of this kernel are of order at most two. As an application we study the indecomposable…

The Zariski theorem says that for every hypersurface in a complex projective (resp. affine) space of dimension at least 3 and for every generic plane in the projective (resp. affine) space the natural embedding generates an isomorphism of…

It is shown that if a finite generically smooth morphism $f\,:\,Y\,\longrightarrow\, X$ of smooth projective varieties induces an isomorphism of the \'etale fundamental groups, then the induced map of the stratified fundamental groups…

According to Bestvina-Bromberg-Fujiwara, a finitely generated group is said to have property (QT) if it acts isometrically on a finite product of quasi-trees so that orbital maps are quasi-isometric embeddings. We prove that the fundamental…

If a finite group $G$ is isomorphic to a subgroup of $SO(3)$, then $G$ has the D2-property. Let $X$ be a finite complex satisfying Wall's D2-conditions. If $\pi_1(X)=G$ is finite, and $\chi(X) \geq 1-Def(G)$, then $X \vee S^2$ is simple…

We address a conjecture that $\pi_1$-surjective maps between closed aspherical 3-manifolds having the same rank on $\pi_1$ must be of non-zero degree. The conjecture is proved for Seifert manifolds, which is used in constructing the first…

The topological fundamental group $\pi_{1}^{top}$ is a topological invariant that assigns to each space a quasi-topological group and is discrete on spaces which are well behaved locally. For a totally path-disconnected, Hausdorff, unbased…

We use Picard-Lefschetz theory to introduce a new local model for the planar projective twists $\tau_{\mathbb{A}\mathbb{P}^2} \in \mathrm{Symp}_{ct}(T^*\mathbb{A}\mathbb{P}^2), \ \mathbb{A} \in \{ \mathbb{R}, \mathbb{C} \}$. In each case,…

This is a technical report accompanying the paper "All Principal Congruence Link Groups" (arXiv:1802.01275) classifying all principal congruence link complements in S^3 by the same authors. It provides a complete overview of all cases (d,I)…

We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…

Generalizing Milnor's result that an FTC (finite total curvature) knot has an isotopic inscribed polygon, we show that any two nearby knotted FTC graphs are isotopic by a small isotopy. We also show how to obtain sharper constants when the…