相关论文: Fundamental Groups of Character Varieties: Surface…

Let S be a surface of genus g with n points removed, G a connected Lie group, and X(G) the moduli space of representations of the fundamental group of S into G. We compute the fundamental group of X(G) when n>0 and G is a real or complex…

We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with at least two type $\bold{E}_6$ singular points. As a simple application, we compute the fundamental groups of 125 other sextics, most of which…

We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities $2\bold{A}_8$ or $\bold{A}_{17}$. We also compute the fundamental groups of a number of other sextics, both of…

We determine the number of connected components of the moduli space for representations of a surface group in the general linear group.

We prove that the complex surfaces parametrizing cuboids and face cuboids, as well as their minimal resolution of singularities, have trivial fundamental group. We then compute the fundamental group of certain open smooth subvarieties of…

We study fundamental groups of algebraic stacks. We show that these fundamental groups carry an additional structure coming from the inertia groups. Then use this additional structure to analyze geometric/ topological properties of stacks.…

This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.

We determine the characters of SL(2) representations of groups and surface groups.

We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n,C) and U(p,q). Our approach relies on the interpretation of these representations in terms of Higgs bundles…

A Lie group is a group that is also a differentiable manifold, such that the group operation is continuous respect to the topological structure. To every Lie group we can associate its tangent space in the identity point as a vector space,…

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

These lecture notes from a first course in algebraic topology use the fundamental group and orbit categories to classify covering spaces.

We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.

Topological characterization of torus groups is given.

We compute the fundamental group of the spaces of ordered commuting $n$-tuples of elements in the Lie groups SU(2), U(2) and SO(3). For SO(3) the computation of the mod-2 cohomology of the components of these spaces is also obtained.

In this note, we present a new method for computing fundamental groups of curve complements using a variation of the Zariski-Van Kampen method on general ruled surfaces. As an application we give an alternative (computation-free) proof for…

The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…

In this paper we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of…

For every finite dimensional Lie group one can consider the group of all smooth loops on it, called its loop group. Such loop groups have long been studied for, among other reasons, their relations to conformal field theories and…

We present a preliminary investigation of algebraic surfaces that have non-planar degenerations, along with their Galois covers and fundamental groups. Specifically, we investigate the tetrahedron and the double tetrahedron. The resulting…