7 citations · 15 across the 9 of their papers we have counts for
14 papers
Uniform spectral gap of scl in -orbifolds
Lvzhou Chen, Nicolaus Heuer
We show a uniform spectral gap of stable commutator length for all compact hyperbolic -orbifolds relative to the peripheral subgroups. Except for the case of a sphere with three…
Voter Model Meets Rumour Spreading: an FPRAS for Consensus Probabilities on Voter Models with Agnostic Nodes
Marcelo Matheus Gauy, Anna Abramishvili, Eduardo Colli +5
Problems of consensus in multi-agent systems are often viewed as a series of independent, simultaneous local decisions made between a limited set of options, all aimed at reaching…
Quasi-BNS invariants
Nicolaus Heuer, Dawid Kielak
We introduce the notion of quasi-BNS invariants, where we replace homomorphism to by homogenous quasimorphisms to in the theory of Bieri-Neumann-Strebel inv…
Stable commutator length in right-angled Artin and Coxeter groups
Lvzhou Chen, Nicolaus Heuer
We establish a spectral gap for stable commutator length (scl) of integral chains in right-angled Artin groups (RAAGs). We show that this gap is not uniform, i.e. there are RAAGs a…
The spectrum of simplicial volume of non-compact manifolds
Nicolaus Heuer, Clara Loeh
We show that, in dimension at least , the set of locally finite simplicial volumes of oriented connected open manifolds is . Moreover, we consider the case of tame…
Computing commutator length is hard
Nicolaus Heuer
The commutator length of an element in the commutator subgroup of a group is the least number of commutators needed to express as their product. If…
Transcendental simplicial volumes
Nicolaus Heuer, Clara Loeh
We show that there exist closed manifolds with arbitrarily small transcendental simplicial volumes. Moreover, we exhibit an explicit uncountable family of (transcendental) real num…
Simplicial volume of one-relator groups and stable commutator length
Nicolaus Heuer, Clara Loeh
A one-relator group is a group that admits a presentation with a single relation . One-relator groups form a rich classically studied class of g…
Spectral gap of scl in graphs of groups and -manifolds
Lvzhou Chen, Nicolaus Heuer
Stable commutator length scl_G(g) of an element g in a group G is an invariant for group elements sensitive to the geometry and dynamics of G. For any group G acting on a tree, we…
The full spectrum of scl on recursively presented groups
Nicolaus Heuer
We show that the set of stable commutator lengths on recursively presented groups equals the set of non-negative right-computable numbers. Hence all non-negative algebra…
The spectrum of simplicial volume
Nicolaus Heuer, Clara Loeh
New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of…
Gaps in scl for Amalgamated Free Products and RAAGs
Nicolaus Heuer
We develop a new criterion to tell if a group has the maximal gap of in stable commutator length (scl). For amalgamated free products we show that every…
Cup Product in Bounded Cohomology of the Free Group
Nicolaus Heuer
The theory of bounded cohomology of groups has many applications. A key open problem is to compute the full bounded cohomology of a non-abelian free group with tr…
Low-dimensional bounded cohomology and extensions of groups
Nicolaus Heuer
Bounded cohomology of groups was first studied by Gromov in 1982. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly c…