7 papers
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…
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…
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…