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Université de Fribourg

Overcommuting pairs in groups and 3-manifolds bounding them

Liechti, Livio ; Marché, Julien

In: Journal of the London Mathematical Society, 2020, p. -

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-manifolds and their Heegaard genus. We give many examples including translations in the affine group of the line and provide upper bounds for the overcommutation length in SL2, related to the Steinberg relation.

Université de Fribourg

Impossibility results on stability of phylogenetic consensus methods

Delucchi, Emanuele ; Hoessly, Linard ; Paolini, Giovanni

In: Systematic Biology, 2020, vol. 69, no. 3, p. 557–565

We answer two questions raised by Bryant, Francis, and Steel in their work on consensus methods in phylogenetics. Consensus methods apply to every practical instance where it is desired to aggregate a set of given phylogenetic trees (say, gene evolution trees) into a resulting, “consensus” tree (say, a species tree). Various stability criteria have been explored in this context, seeking...

Université de Fribourg

Dorronsoro’s theorem in Heisenberg groups

Fässler, Katrin ; Orponen, Tuomas

In: Bulletin of the London Mathematical Society, 2020, vol. 52, no. 3, p. 472–488

A theorem of Dorronsoro from the 1980s quantifies the fact that real‐valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of Dorronsoro's theorem in Heisenberg groups: functions in horizontal Sobolev spaces can be approximated by affine functions which are independent of the last...

Université de Fribourg

Fundamental polytopes of metric trees via parallel connections of matroids

Delucchi, Emanuele ; Hoessly, Linard

In: European Journal of Combinatorics, 2020, vol. 87, p. 103098

We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik (2010).In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid.- We give explicit formulas for the face numbers of fundamental polytopes and ...

Université de Fribourg

Locally homogeneous aspherical Sasaki manifolds

Baues, Oliver ; Kamishima, Yoshinobu

In: Differential Geometry and its Applications, 2020, vol. 70, p. 101607

Université de Fribourg

Canonical parameterizations of metric disks

Lytchak, Alexander ; Wenger, Stefan

In: Duke Mathematical Journal, 2020, vol. 169, no. 4, p. 761–797

We use the recently established existence and regularity of area and energy minimizing disks in metric spaces to obtain canonical parameterizations of metric surfaces. Our approach yields a new and conceptually simple proof of a well-known theorem of Bonk and Kleiner on the existence of quasisymmetric parameterizations of linearly locally connected, Ahlfors 2-regular metric 2-spheres....

Université de Fribourg

Metric currents and polylipschitz forms

Pankka, Pekka ; Soultanis, Elefterios

In: Calculus of Variations and Partial Differential Equations, 2020, vol. 59, no. 2, p. 76

Université de Fribourg

Ideal polyhedral surfaces in Fuchsian manifolds

Prosanov, Roman

In: Geometriae Dedicata, 2020, vol. 206, no. 1, p. 151–179

Let Sg,n be a surface of genus g>1 with n>0 punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a new variational proof of this result. We also give an alternative proof of the existence and uniqueness of a hyperbolic polyhedral metric with prescribed curvature in a...