Deformations of large fundamental groups

Deformations of large fundamental groups

Quantum Deformations of Fundamental Groups of Oriented 3-manifolds

We compute two-term skein modules of framed oriented links in oriented 3-manifolds. They contain the self-writhe and total linking number invariants of framed oriented links in a universal way. The relations in a natural presentation of the skein module are interpreted as monodromies in the space of immersions of circles into the 3-manifold.

Deformations of representations of fundamental groups of open Kähler manifolds

Given a compact Kähler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of π1(U) with certain restrictions related to the divisor. We show that the possible singularities of this variety as well as of the corresponding moduli space of irreducible representations are quadratic. In the course of our proof we exhibit a diffe...

Irreducible Plane Sextics with Large Fundamental Groups

We compute the fundamental group of the complement of each irreducible sextic of weight eight or nine (in a sense, the largest groups for irreducible sextics), as well as of 169 of their derivatives (both of and not of torus type). We also give a detailed geometric description of sextics of weight eight and nine and of their moduli spaces and compute their Alexander modules; the latter are show...

Fundamental Functor Based on Hypergroups and Groups

The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundam...