Michael Brandenbursky

activity

20092026

most citedCancelation norm and the geometry of biinvariant word metrics

17 citations · 71 across the 20 of their papers we have counts for

collaborators

32 papers

math.GT2026

Bounded cohomology of transformation groups in all degrees

Michael Brandenbursky

Let $M$ be a compact connected oriented smooth manifold, of dimension $n \geq 2$ . Let $T_{M} G$ be one of the following transformation groups: $H o m e o_{0} (M, μ)$ , $D i f f_{0} (M, μ)$ , $Sy…

math.GT2025

On quasimorphisms and distortion in homeomorphism groups

Michael Brandenbursky, Jarek Kedra, Michal Marcinkowski +1

Let $M$ be a smooth compact oriented connected manifold, and $Homeo_{0} (M, μ)$ the group of homeomorphisms of $M$ supported away from $\partial M,$ which preserve a Borel probab…

math.GT2025

The $L^{p}$ -diameter of the space of contractible loops

Michael Brandenbursky, Egor Shelukhin

We prove that the space of contractible simple loops of a given fixed area in any compact oriented surface has infinite diameter as a homogeneous space of the group of area-preserv…

math.GT2025

Bounded cohomology of measure-preserving homeomorphism groups of non-orientable surfaces

Michael Brandenbursky, Lior Menashe

Let $N_{g}$ be a closed non-orientable surface of genus $g \geq 3$ , and let $Homeo_{0} (N_{g}, μ)$ be the identity component of its group of measure-preserving homeomorphisms.…

math.GT2023

Volume and Euler classes in bounded cohomology of transformation groups

Michael Brandenbursky, Michał Marcinkowski

Let $M$ be an oriented smooth manifold, and $Homeo (M, ω)$ the group of measure preserving homeomorphisms of $M$ , where $ω$ is a finite measure induced by a volume for…

math.DG2022★ 3 cited

Non-commutative Barge-Ghys quasimorphisms: an erratum

Michael Brandenbursky, Misha Verbitsky

This is an erratum to the paper ``Non-commutative Barge-Ghys quasimorphisms''. The effective version of Ambrose-Singer theorem used in this paper was mis-stated, making Theorem 3.1…

math.DS2021

$C^{0}$ -gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of surfaces

Michael Brandenbursky, Michael Khanevsky

Let $Σ$ be a surface equipped with an area form. There is an long standing open question by Katok, which, in particular, asks whether every entropy-zero Hamiltonian diffeomorphism…

math.GT2021

The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms

Michael Brandenbursky, Michał Marcinkowski, Egor Shelukhin

We prove a number of new results on the large-scale geometry of the $L^{p}$ -metrics on the group of area-preserving diffeomorphisms of each orientable surface. Our proofs use in a ke…

math.AG2020

Lipschitz geometry of surface germs in $R^{4}$ : metric knots

Lev Birbrair, Michael Brandenbursky, Andrei Gabrielov

A link at the origin of an isolated singularity of a two-dimensional semialgebraic surface in $R^{4}$ is a topological knot (or link) in $S^{3}$ . We study the connection betwe…

math.GT2019

On the entropy norm on $H am (S^{2})$

Michael Brandenbursky, Egor Shelukhin

In this note we prove that for each positive integer $m$ there exists a bi-Lipschitz embedding $Z^{m} \to H am (S^{2})$ , where $H am (S^{2})$ is equipped with the entropy metric. In particula…

math.GT2019

Bounded cohomology of transformation groups

Michael Brandenbursky, Michal Marcinkowski

Let $M$ be a complete connected Riemannian manifold of finite volume. In this paper we present a new method of constructing classes in bounded cohomology of transformation groups s…

math.GT2018

Fragmentation norm and relative quasimorphisms

Michael Brandenbursky, Jarek Kędra

We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm with respect to balls of bou…

math.GT2018

On the entropy norm on the group of diffeomorphisms of closed oriented surface

Michael Brandenbursky, Arpan Kabiraj

We prove that the entropy norm on the group of diffeomorphisms of a closed orientable surface of positive genus is unbounded.

math.GT2017

Entropy and quasimorphisms

Michael Brandenbursky, Michał Marcinkowski

Let $S$ be a compact oriented surface. We construct homogeneous quasimorphisms on $D i f f (S, a r e a)$ , on $D i f f_{0} (S, a r e a)$ and on $H am (S)$ generalizing the constructions of Gambaudo-G…

math.GT2017

Aut-invariant norms and Aut-invariant quasimorphisms on free and surface groups

Michael Brandenbursky, Michał Marcinkowski

Let $F_{n}$ be the free group on $n$ generators and $Γ_{g}$ the surface group of genus $g$ . We consider two particular generating sets: the set of all primitive elements in $F_{n}$ and t…

math.GT2016

Concordance of certain 3-braids and Gauss diagrams

Michael Brandenbursky

Let $β := σ_{1} σ_{2}^{- 1}$ be a braid in $B_{3}$ , where $B_{3}$ is the braid group on 3 strings and $σ_{1}, σ_{2}$ are the standard Artin generators. We use Gauss diagram formulas to show that f…

math.GT2016★ 6 cited

The $L^{p}$ -diameter of the group of area-preserving diffeomorphisms of $S^{2}$

Michael Brandenbursky, Egor Shelukhin

We show that for each $p \geq 1,$ the $L^{p}$ -metric on the group of area-preserving diffeomorphisms of the two-sphere has infinite diameter. This solves the last open case of a conj…

math.SG2016

The autonomous norm on $H am (R^{2 n})$ is bounded

Michael Brandenbursky, Jarek Kędra

We prove that the autonomous norm on the group of compactly supported Hamiltonian diffeomorphisms of the standard $R^{2 n}$ is bounded.

math.SG2016

On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus

Michael Brandenbursky, Jarek Kedra, Egor Shelukhin

We prove that the autonomous norm on the group of Hamiltonian diffeomorphisms of the two-dimensional torus is unbounded. We provide explicit examples of Hamiltonian diffeomorphisms…

math.SG2014

On the $L^{p}$ -geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky, Egor Shelukhin

We prove a number of results on the interrelation between the $L^{p}$ -metric on the group of Hamiltonian diffeomorphisms of surfaces and the subset of all autonomous Hamiltonian diff…

math.GT2014★ 7 cited

Concordance group and stable commutator length in braid groups

Michael Brandenbursky, Jarek Kędra

We define a quasihomomorphism from braid groups to the concordance group of knots and examine its properties and consequences of its existence. In particular, we provide a relation…

math.GT2013★ 17 cited

Cancelation norm and the geometry of biinvariant word metrics

Michael Brandenbursky, Światosław R. Gal, Jarek Kędra +1

We study biinvariant word metrics on groups. We provide an efficient algorithm for computing the biinvariant word norm on a finitely generated free group and we construct an isomet…

math.GT2013

Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky

Let Σ_g be a closed orientable surface let Diff_0(Σ_g; area) be the identity component of the group of area-preserving diffeomorphisms of Σ_g. In this work we present an extension…

math.GT2013

On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces

Michael Brandenbursky

Let $Σ_{g}$ be a closed hyperbolic surface of genus $g$ and let $H am (Σ_{g})$ be the group of Hamiltonian diffeomorphisms of $Σ_{g}$ . The most natural word metric on this group is the aut…

Bounded cohomology of transformation groups in all degrees

On quasimorphisms and distortion in homeomorphism groups

The Lp-diameter of the space of contractible loops

Bounded cohomology of measure-preserving homeomorphism groups of non-orientable surfaces

Volume and Euler classes in bounded cohomology of transformation groups

Non-commutative Barge-Ghys quasimorphisms: an erratum

C0-gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of surfaces

The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms

Lipschitz geometry of surface germs in R4: metric knots

On the entropy norm on Ham(S2)

Bounded cohomology of transformation groups

Fragmentation norm and relative quasimorphisms

On the entropy norm on the group of diffeomorphisms of closed oriented surface

Entropy and quasimorphisms

Aut-invariant norms and Aut-invariant quasimorphisms on free and surface groups

Concordance of certain 3-braids and Gauss diagrams

The Lp-diameter of the group of area-preserving diffeomorphisms of S2

The autonomous norm on Ham(R2n) is bounded

On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus

On the Lp-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Concordance group and stable commutator length in braid groups

Cancelation norm and the geometry of biinvariant word metrics

Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces

On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces

The $L^{p}$ -diameter of the space of contractible loops

$C^{0}$ -gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of surfaces

Lipschitz geometry of surface germs in $R^{4}$ : metric knots

On the entropy norm on $H am (S^{2})$

The $L^{p}$ -diameter of the group of area-preserving diffeomorphisms of $S^{2}$

The autonomous norm on $H am (R^{2 n})$ is bounded

On the $L^{p}$ -geometry of autonomous Hamiltonian diffeomorphisms of surfaces