0000000000007661
AUTHOR
Luisa Paoluzzi
showing 13 related works from this author
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.
A note on the Lawrence-Krammer-Bigelow representation
2002
A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.
Commensurability classification of a family of right-angled Coxeter groups
2008
We classify the members of an infinite family of right-angled Coxeter groups up to abstract commensurability.
On cyclic branched coverings of prime knots
2007
We prove that a prime knot K is not determined by its p-fold cyclic branched cover for at most two odd primes p. Moreover, we show that for a given odd prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold cyclic branched cover of at most one more knot K' non equivalent to K. To prove the main theorem, a result concerning the symmetries of knots is also obtained. This latter result can be interpreted as a characterisation of the trivial knot.
Conway irreducible hyperbolic knots with two common covers
2005
International audience; For each pair of coprime integers n > m ≥ 2 we construct pairs of non equivalent Conway irreducible hyperbolic knots with the same n-fold and m-fold cyclic branched covers.
Hyperbolic knots and cyclic branched covers
2021
International audience; We collect several results on the determination of hyperbolic knots by means of their cyclic branched covers. We construct examples of knots having two common cyclic branched covers. Finally, we brie y discuss the problem of determination of hyperbolic links
Hyperbolic isometries versus symmetries of links
2009
We prove that every finite group is the orientation-preserving isometry group of the complement of a hyperbolic link in the 3-sphere.
On the classification of CAT(0) structures for the 4-string braid group
2005
This paper is concerned with the class of so-called CAT(0) groups, namely, those groups that admit a geometric (i.e., properly discontinuous, co-compact, and isometric) action on some CAT(0) space. More precisely, we are interested in knowing to what extent it is feasible to classify the geometric CAT(0) actions of a given group (up to, say, equivariant homothety of the space). A notable example of such a classification is the flat torus theorem, which implies that the minimal geometric CAT(0) actions of the free abelian group Z (n ≥ 1) are precisely the free actions by translations of Euclidean space E. Typically, however, a given group will have uncountably many nonequivalent actions, mak…
3-manifolds which are orbit spaces of diffeomorphisms
2008
Abstract In a very general setting, we show that a 3-manifold obtained as the orbit space of the basin of a topological attractor is either S 2 × S 1 or irreducible. We then study in more detail the topology of a class of 3-manifolds which are also orbit spaces and arise as invariants of gradient-like diffeomorphisms (in dimension 3). Up to a finite number of exceptions, which we explicitly describe, all these manifolds are Haken and, by changing the diffeomorphism by a finite power, all the Seifert components of the Jaco–Shalen–Johannson decomposition of these manifolds are made into product circle bundles.
Non-equivalent hyperbolic knots
2002
We construct, for each integer n 3, pairs of non-equivalent hyperbolic knots with the same 2fold and n-fold cyclic branched covers. We also discuss necessary conditions for such pairs of knots to exist. 2001 Elsevier Science B.V. All rights reserved. MSC: primary 57M25; secondary 57M12, 57M50
On the classification of Kim and Kostrikin manifolds
2006
International audience; We completely classify the topological and geometric structures of some series of closed connected orientable 3-manifolds introduced by Kim and Kostrikin in [20, 21] as quotient spaces of certain polyhedral 3-cells by pairwise identifications of their boundary faces. Then we study further classes of closed orientable 3-manifolds arising from similar polyhedral schemata, and describe their topological properties.
Non equivalent hyperbolic knots
2002
International audience
Erratum to On π-hyperbolic knots and branched coverings
2005
International audience