# Profinite rigidity of fibring

@inproceedings{Hughes2022ProfiniteRO, title={Profinite rigidity of fibring}, author={Sam Hughes and Dawid Kielak}, year={2022} }

. We introduce the classes of TAP groups, in which various types of algebraic ﬁbring are detected by the non-vanishing of twisted Alexander polynomials. We show that ﬁnitely presented LERF groups lie in the class TAP 1 ( R ) for every integral domain R , and deduce that algebraic ﬁbring is a proﬁnite property for such groups. We oﬀer stronger results for algebraic ﬁbring of products of limit groups, as well as applications to proﬁnite rigidity of Poincaré duality groups in dimension 3 and RFRS…

## References

SHOWING 1-10 OF 85 REFERENCES

### Fisher

- Improved algebraic fibrings,
- 2021

### FINITE-VOLUME HYPERBOLIC 3-MANIFOLDS ARE ALMOST DETERMINED BY THEIR FINITE QUOTIENT GROUPS

- Mathematics
- 2020

For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral…

### Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups

- MathematicsInventiones mathematicae
- 2022

For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral…

### Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices

- Mathematics
- 2022

We prove that in a cocompact complex hyperbolic arithmetic lattice Γ < PU( m, 1) of the simplest type, deep enough ﬁnite index subgroups admit plenty of homomorphisms to Z with kernel of type F m − 1…

### Algebraic fibrings of hyperbolic manifolds

- Mathematics
- 2022

We prove that there are finite-volume, hyperbolic manifolds of dimensions 6, 7, and 8 that algebraically fibre with kernel of type FP2(Q), F2 and FP(Q), and F2 and FP3(Q), respectively. The manifolds…

### Irreducible lattices fibring over the circle

- Mathematics
- 2022

We investigate the Bieri--Neumann--Strebel--Renz (BNSR) invariants of irreducible uniform lattices in the product of Isom(𝔼n) and Aut(T) or Aut(S˜L), where T is locally finite tree and S˜L is the…

### Improved algebraic fibrings

- Mathematics
- 2021

We show that a virtually RFRS group G of type FPn(Q) virtually algebraically fibres with kernel of type FPn(Q) if and only if the first n l2Betti numbers of G vanish, that is, b (2) p (G) = 0 for 0 6…

### Hyperbolic 5-manifolds that fiber over $$S^1$$

- MathematicsInventiones mathematicae
- 2022

We exhibit some finite-volume cusped hyperbolic 5-manifolds that fiber over the circle. These include the smallest hyperbolic 5-manifold known, discovered by Ratcliffe and Tschantz. As a consequence,…

### Hyperbolic manifolds that fiber algebraically up to dimension 8

- Mathematics
- 2020

We construct some cusped finite-volume hyperbolic $n$-manifolds $M_n$ that fiber algebraically in all the dimensions $5\leq n \leq 8$. That is, there is a surjective homomorphism $\pi_1(M_n) \to…