28 citations · 49 across the 17 of their papers we have counts for
22 papers
Profinite recognition of uniformity
Holger Kammeyer
Let be a semisimple Lie group that is not isogenous to the isometry group of real or complex hyperbolic -space. We show that the rational rank is a profinite invariant for i…
A counterexample to the determinant approximation conjecture
Holger Kammeyer
The determinant approximation conjecture states that for a residually finite group and a chain of finite index normal subgroups with trivial intersection, the Fuglede-Kad…
Congruence rigidity of algebraic groups
Adrian Baumann, Holger Kammeyer
We identify the simple algebraic groups over number fields that are, in a suitable sense, determined by their finite adele points. Assuming CSP and Grothendieck rigidity, our resul…
Infinite groups from the profinite point of view
Holger Kammeyer, Steffen Kionke
We survey recent work ranging around the question in how far a group, or a property of a group, is determined by the set of finite quotient groups. Our focus lies on -arithmetic…
Profiniteness of higher rank volume
Holger Kammeyer, Steffen Kionke, Ralf Köhl
We show that the covolume of an irreducible lattice in a higher rank semisimple Lie group with the congruence subgroup property is determined by the profinite completion. Without r…
On the Euler characteristic of -arithmetic groups
Holger Kammeyer, Giada Serafini
We show that the sign of the Euler characteristic of an -arithmetic subgroup of a simple algebraic group depends on the -congruence completion only, except possibly in type $…
Gassmann triples with special cycle types and applications
Holger Kammeyer, Steffen Kionke
We show that if one of various cycle types occurs in the permutation action of a finite group on the cosets of a given subgroup, then every almost conjugate subgroup is conjugate.…
Bounded cohomology is not a profinite invariant
Daniel Echtler, Holger Kammeyer
We construct pairs of residually finite groups with isomorphic profinite completions such that one has non-vanishing and the other has vanishing real second bounded cohomology. The…
Galois cohomology and profinitely solitary Chevalley groups
Holger Kammeyer, Ryan Spitler
For every number field and every Cartan Killing type, there is an associated split simple algebraic group. We examine whether the corresponding arithmetic subgroups are profinitely…
On absolutely profinitely solitary lattices in higher rank Lie groups
Holger Kammeyer
We establish conditions under which lattices in certain simple Lie groups are profinitely solitary in the absolute sense, so that the commensurability class of the profinite comple…
Adelic superrigidity and profinitely solitary lattices
Holger Kammeyer, Steffen Kionke
By arithmeticity and superrigidity, a commensurability class of lattices in a higher rank Lie group is defined by a unique algebraic group over a unique number subfield of $\mathbb…
On the profinite rigidity of lattices in higher rank Lie groups
Holger Kammeyer, Steffen Kionke
We investigate which higher rank simple Lie groups admit profinitely but not abstractly commensurable lattices. We show that no such examples exist for the complex forms of type $E…
Products of free groups in Lie groups
Caterina Campagnolo, Holger Kammeyer
For every Lie group , we compute the maximal such that an -fold product of nonabelian free groups embeds into .
Profinite invariants of arithmetic groups
Holger Kammeyer, Steffen Kionke, Jean Raimbault +1
We prove that the sign of the Euler characteristic of arithmetic groups with CSP is determined by the profinite completion. In contrast, we construct examples showing that this is…
S-arithmetic spinor groups with the same finite quotients and distinct -cohomology
Holger Kammeyer, Roman Sauer
In this note we refine examples by Aka from arithmetic to S-arithmetic groups to show that the vanishing of the -th -Betti number is not a profinite invariant for all $i…
A remark on torsion growth in homology and volume of 3-manifolds
Holger Kammeyer
We show that Lück's conjecture on torsion growth in homology implies that two 3-manifolds have equal volume if the fundamental groups have the same set of finite quotients.
Profinite commensurability of S-arithmetic groups
Holger Kammeyer
Given an S-arithmetic group, we ask how much information on the ambient algebraic group, number field of definition, and set of places S is encoded in the commensurability class of…
The shrinkage type of knots
Holger Kammeyer
We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated…
Approximating Novikov-Shubin numbers of virtually cyclic coverings
Holger Kammeyer
We assign real numbers to finite sheeted coverings of compact CW complexes designed as finite counterparts to the Novikov-Shubin numbers. We prove an approximation theorem in the c…
The Farrell-Jones conjecture for arbitrary lattices in virtually connected Lie groups
Holger Kammeyer, Wolfgang Lueck, Henrik Rueping
We prove the K- and the -theoretic Farrell-Jones conjecture with coefficients in additive categories and with finite wreath products for arbitrary lattices in virtually connecte…
L2-invariants of nonuniform lattices in semisimple Lie groups
Holger Kammeyer
We compute L2-invariants of certain nonuniform lattices in semisimple Lie groups by means of the Borel-Serre compactification of arithmetically defined locally symmetric spaces. Th…
An explicit rational structure for real semisimple Lie algebras
Holger Kammeyer
We construct a convenient basis for all real semisimple Lie algebras by means of an adapted Chevalley basis of the complexification. It determines rational and in fact half-integer…