A branch set linking theorem.
A Hopf Inequality for Branch Sets.
A Note on Hyperbolic 3-Manifolds of the Same Volume.
A short proof of Eilenberg and Moore’s theorem
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
A Splitting Theorem for Manifolds.
All Knot Groups Are Metric.
An analogue of covering space theory for ranked posets.
An Exact Sequence of Braid Groups.
An introduction to the abelian Reidemeister torsion of three-dimensional manifolds
These notes accompany some lectures given at the autumn school “Tresses in Pau” in October 2009. The abelian Reidemeister torsion for -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.
Braid Monodromy of Algebraic Curves
These are the notes from a one-week course on Braid Monodromy of Algebraic Curves given at the Université de Pau et des Pays de l’Adour during the Première Ecole Franco-Espagnole: Groupes de tresses et topologie en petite dimension in October 2009.This is intended to be an introductory survey through which we hope we can briefly outline the power of the concept monodromy as a common area for group theory, algebraic geometry, and topology of projective curves.The main classical results are stated...
Branched Immersions of Surfaces and Reduction of Topological Type, I.
Branched Immersions of Surfaces and Reduction of Topological Type. II.
Classifying finite-sheeted covering mappings of paracompact spaces.
The main result of the present paper is a classification theorem for finite-sheeted covering mappings over connected paracompact spaces. This theorem is a generalization of the classical classification theorem for covering mappings over a connected locally pathwise connected semi-locally 1-connected space in the finite-sheeted case. To achieve the result we use the classification theorem for overlay structures which was recently proved by S. Mardesic and V. Matijevic (Theorems 1 and 4 of [5]).
Compactifying coverings of 3-manifolds.
Complete Homogeneous Riemannian Manifolds of Negative Sectional Curvature.
Conjugacy Relations in Subgroups of the Mapping Class Group and a Group-Theoretic Description of the Rochlin Invariant.
Constructing and forbidding automorphisms in lifted maps
Covering maps over solenoids which are not covering homomorphisms
Let Y be a connected group and let f: X → Y be a covering map with the total space X being connected. We consider the following question: Is it possible to define a topological group structure on X in such a way that f becomes a homomorphism of topological groups. This holds in some particular cases: if Y is a pathwise connected and locally pathwise connected group or if f is a finite-sheeted covering map over a compact connected group Y. However, using shape-theoretic techniques and Fox's notion...
Coverings of fibrations
Coverings of stably parallelizable manifolds