151 citations · 682 across the 59 of their papers we have counts for
72 papers
Euler's work on spherical geometry: An overview with comments
Athanase Papadopoulos, Vladimir Turaev
We review Euler's work on spherical geometry. After an introduction concerning the general place that trigonometric formulae occupy in geometry, we start by the two memoirs of Eule…
Strings in metric spaces
Vladimir Turaev
We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite me…
Knots and links in 2-complexes
Vladimir Turaev
We introduce and study knots and links in 2-dimensional complexes. In particular, we define linking numbers for oriented two-component links in 2-complexes and a Kauffman-type brac…
Multi-quandles of topological pairs
Vladimir Turaev
In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected…
Quasi-Lie bialgebras of loops in quasi-surfaces
Vladimir Turaev
We discuss natural operations on loops in a quasi-surface and show that these operations define a structure of a quasi-Lie bialgebra in the module generated by the set of free homo…
Quasi-Poisson structures on moduli spaces of quasi-surfaces
Vladimir Turaev
In generalization of the classical Atiyah-Bott Poisson brackets on the moduli spaces of surfaces we define quasi-Poisson brackets on the moduli spaces of quasi-surfaces.