Let K be a finite simplicial complex, and (X,A) be a pair of spaces. The purpose of this article is to study the fundamental group of the polyhedral product denoted ZK(X,A), which denotes the moment-angle complex of Buchstaber-Panov in the case (X,A) = (D2, S1), with extension to arbitrary pairs

of the above examples and interprets their symplectic structures in terms of the inter-section pairing on the surface. Our setup is as follows. Consider a closed oriented topological surface S with fundamental group rt and let G be a connected Lie group. The space Hom(n, G) consisting of representations rr + G

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This paper is devoted to the study of a natural group topology on the fundamental group which remembers local properties of spaces forgotten by covering space theory and weak homotopy type. It is known that viewing the fundamental group as the quotient of the loop space often fails to result in a

ABSTRACT: In this paper we will discuss the dynamical graph and its fundamental group. Also we will study the folding of the dynamical graph and the change of the fundamental group under the folding. The variation of the fundamental group under the variation of time will be discussed. We will study

Abstract. 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. We give an explicit formula for the fundamental

Abstract. We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with at least two type E6 singular points. As a simple application, we compute the fundamental groups of 125 other sextics, most of which are new. 1.

Abstract. A proof of freeness of the commutator subgroup of the fundamental group of a smooth irreducible affine curve over an algebraically closed field of nonzero characteristic. A description of the abelianizations of the fundamental groups of affine curves over an algebraically closed field

Abstract. A proof of freeness of the commutator subgroup of the fundamental group of a smooth irreducible affine curve over a countable algebraically closed field of nonzero characteristic. A description of the abelianizations of the fundamental groups of affine curves over an algebraically closed