25 citations · 61 across the 22 of their papers we have counts for
25 papers
The orientation-reversing minimal stretch factor problem in small genus
Pierre Dehornoy, Erwan Lanneau, Livio Liechti +1
We determine the minimal stretch factors among all orientation-reversing pseudo-Anosov mapping classes of the closed orientable surfaces of genus two, three and four.
Trace field degrees in the Torelli group
Erwan Lanneau, Livio Liechti
We show that for , all integers arise as trace field degrees of pseudo-Anosov mapping classes in the Torelli group of the closed orientable surface of ge…
Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps
Erwan Lanneau, Livio Liechti, Chi Cheuk Tsang
We show that the stretch factor of an orientation-reversing fully-punctured pseudo-Anosov map on a finite-type orientable surface , with and having at…
On the signature of a positive braid
Joshua Evan Greene, Livio Liechti
We show that the signature of a positive braid link is bounded from below by one-quarter of its first Betti number. This equates to one-half of the optimal bound conjectured by Fel…
On the minimal spectral radii of skew-reciprocal integer matrices
Livio Liechti
We determine the minimal spectral radii among all skew-reciprocal integer matrices of a fixed even dimension that are primitive or nonnegative and irreducible. In particular, excep…
Trace field degrees of Abelian differentials
Erwan Lanneau, Livio Liechti
We prove that every even number is realised as the degree of a Thurston-Veech pseudo-Anosov stretch factor in every connected component of every stratum of the mo…
Minor theory for quasipositive surfaces
Sebastian Baader, Pierre Dehornoy, Livio Liechti
The set of quasipositive surfaces is closed under incompressible inclusion. We prove that the induced order on fibre surfaces of positive braid links is almost a well-quasi-order.…
The geometry of bi-Perron numbers with real or unimodular Galois conjugates
Livio Liechti, Joshua Pankau
Among all bi-Perron numbers, we characterise those all of whose Galois conjugates are real or unimodular as the ones that admit a power which is the stretch factor of a pseudo-Anos…
Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups
Ruth Kellerhals, Livio Liechti
We show that not every Salem number appears as the growth rate of a cocompact hyperbolic Coxeter group. We also give a new proof of the fact that the growth rates of planar hyperbo…
Divide knots of maximal genus defect
Livio Liechti
We construct divide knots with arbitrary smooth four-genus but topological four-genus equal to one. In particular, for strongly quasipositive fibred knots, the ratio between the to…
Divide monodromies and antitwists on surfaces
Pierre Dehornoy, Livio Liechti
A divide on an orientable 2-orbifold gives rise to a fibration of the unit tangent bundle to the orbifold.We characterize the corresponding monodromies as exactly the products of a…
Overcommuting pairs in groups and 3-manifolds bounding them
Livio Liechti, Julien Marché
We introduce the notions of overcommutation and overcommutation length in groups, and show that these concepts are closely related to representations of the fundamental groups of 3…
On the arithmetic and the geometry of skew-reciprocal polynomials
Livio Liechti
We reformulate Lehmer's question from 1933 and a question due to Schinzel and Zassenhaus from 1965 in terms of a comparison of the Mahler measures and the houses, respectively, of…
Minimal Penner dilatations on nonorientable surfaces
Livio Liechti, Balázs Strenner
For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner's construction. We deduce that the sequence of min…
Minimal pseudo-Anosov stretch factors on nonoriented surfaces
Livio Liechti, Balázs Strenner
We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed nonorientable surfaces of genus 4, 5, 6, 7, 8, 10, 12, 14, 16…
On the genus defect of positive braid knots
Livio Liechti
We show that the difference between the Seifert genus and the topological 4-genus of a prime positive braid knot is bounded from below by an affine function of the minimal number o…
The Arnoux-Yoccoz mapping classes via Penner's construction
Livio Liechti, Balázs Strenner
We give a new description of the Arnoux-Yoccoz mapping classes as a product of two Dehn twists and a finite order element. The construction is analogous to Penner's construction of…
Checkerboard graph monodromies
Sebastian Baader, Lukas Lewark, Livio Liechti
We associate an open book with any connected plane checkerboard graph, thus providing a common extension of the classes of prime positive braid links and positive tree-like Hopf pl…
Teichmüller polynomials of fibered alternating links
Robert Billet, Livio Liechti
We give an algorithm for computing the Teichmüller polynomial for a certain class of fibered alternating links associated to trees. Furthermore, we exhibit a mutant pair of such li…
Minimal dilatation in Penner's construction
Livio Liechti
For all orientable closed surfaces, we determine the minimal dilatation among mapping classes arising from Penner's construction. We also discuss generalisations to surfaces with p…
Positive braid knots of maximal topological 4-genus
Livio Liechti
We show that a positive braid knot has maximal topological 4-genus exactly if it has maximal signature invariant. As an application, we determine all positive braid knots with maxi…
On the topological 4-genus of torus knots
Sebastian Baader, Peter Feller, Lukas Lewark +1
We prove that the topological locally flat slice genus of large torus knots takes up less than three quarters of the ordinary genus. As an application, we derive the best possible…
On Coxeter mapping classes and fibered alternating links
Eriko Hironaka, Livio Liechti
Alternating-sign Hopf plumbing along a tree yields fibered alternating links whose homological monodromy is, up to a sign, conjugate to some alternating-sign Coxeter transformation…
Signature and concordance of positive knots
Sebastian Baader, Pierre Dehornoy, Livio Liechti
We derive a linear estimate of the signature of positive knots, in terms of their genus. As an application, we show that every knot concordance class contains at most finitely many…