Search results for "Mathematics::Geometric Topology"
showing 10 items of 117 documents
Equidistribution and Counting of Common Perpendiculars in Quotient Spaces
2019
In this chapter, we use the results of Chapter 11 to prove equidistribution and counting results in Riemannian manifolds (or good orbifolds) and in metric and simplicial graphs (of groups).
Braiding minimal sets of vector fields
2002
We extend a classical but fundamental theorem of knot and braid theories to describe the geometry of nonsingular minimal sets of 3-dimensional flows.
Conjugacy problem for braid groups and Garside groups
2003
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).
Boundary behavior of quasi-regular maps and the isodiametric profile
2001
We study obstructions for a quasi-regular mapping f : M → N f:M\rightarrow N of finite degree between Riemannian manifolds to blow up on or collapse on a non-trivial part of the boundary of M M .
Conjugate unstable manifolds and their underlying geometrized Markov partitions
2000
Abstract Conjugate unstable manifolds of saturated hyperbolic sets of Smale diffeomorphisms are characterized in terms of the combinatorics of their geometrized Markov partitions. As a consequence, the relationship between the local and the global point of view is also made explicit.
Transitive partially hyperbolic diffeomorphisms on 3-manifolds
2005
Abstract The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds belong to 3 basic classes: perturbations of skew products over an Anosov map of T 2 , perturbations of the time one map of a transitive Anosov flow, and certain derived from Anosov diffeomorphisms of the torus T 3 . In this work we characterize the two first types by a local hypothesis associated to one closed periodic curve.
Three cyclic branched covers suffice to determine hyperbolic knots.
2005
Let n > m > 2 be two fixed coprime integers. We prove that two Conway reducible, hyperbolic knots sharing the 2-fold, m-fold and n-fold cyclic branched covers are equivalent. Using previous results by Zimmermann we prove that this implies that a hyperbolic knot is determined by any three of its cyclic branched covers.
Synthetic electromagnetic knot in a three-dimensional skyrmion
2018
We experimentally simulate a quantum-mechanical particle interacting with knotted electromagnetic fields.
A cubic defining algebra for the Links–Gould polynomial
2013
Abstract We define a finite-dimensional cubic quotient of the group algebra of the braid group, endowed with a (essentially unique) Markov trace which affords the Links–Gould invariant of knots and links. We investigate several of its properties, and state several conjectures about its structure.
Real quadrics in C n , complex manifolds and convex polytopes
2006
In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics Cn which are invariant with respect to the natural action of the real torus (S1)n onto Cn. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-cros…