7 papers
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.