6 papers · 1 filter
On a twisted Singer conjecture
Jacopo G. Chen
According to the Singer conjecture, the -Betti numbers of a closed aspherical manifold are expected to vanish outside the middle dimension. In this paper, we study a natural a…
Some closed hyperbolic 5-manifolds
Jacopo G. Chen
We give an explicit construction of a family of closed arithmetic hyperbolic 5-manifolds, tessellated by copies of a Coxeter simplicial pri…
Closed hyperbolic manifolds without structures
Jacopo G. Chen
In all dimensions , we prove the existence of closed orientable hyperbolic manifolds that do not admit any structure, and in fact we show that there are in…
Non-cobordant hyperbolic manifolds
Jacopo G. Chen
In all dimensions not of the form , we show that there exists a closed hyperbolic -manifold which is not the boundary of a compact -manifold. The proof re…
Cusp-transitive 4-manifolds with every cusp section
Jacopo Guoyi Chen, Edoardo Rizzi
We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, f…
Computing the twisted -Euler characteristic
Jacopo G. Chen
We present an algorithm that computes Friedl and Lück's twisted -Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirect…