J. G. Chen

collaborators

5 papers

math.GT2026

On a twisted Singer conjecture

Jacopo G. Chen

According to the Singer conjecture, the $L^{2}$ -Betti numbers of a closed aspherical manifold are expected to vanish outside the middle dimension. In this paper, we study a natural a…

math.GT2025

Computing the twisted $L^{2}$ -Euler characteristic

Jacopo G. Chen

We present an algorithm that computes Friedl and LÃ¼ck's twisted $L^{2}$ -Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirec…

math.GT2025

Some closed hyperbolic 5-manifolds

Jacopo G. Chen

We give an explicit construction of a family of closed arithmetic hyperbolic 5-manifolds, tessellated by $117964800 = 512 \cdot 16 \cdot 14400$ copies of a Coxeter simplicial pri…

math.GT2025

Closed hyperbolic manifolds without $spin^{c}$ structures

Jacopo G. Chen

In all dimensions $n \geq 5$ , we prove the existence of closed orientable hyperbolic manifolds that do not admit any $spin^{c}$ structure, and in fact we show that there are in…

math.GT2025

Non-cobordant hyperbolic manifolds

Jacopo G. Chen

In all dimensions $n \geq 4$ not of the form $4 m + 3$ , we show that there exists a closed hyperbolic $n$ -manifold which is not the boundary of a compact $(n + 1)$ -manifold. The proof re…

On a twisted Singer conjecture

Computing the twisted L2-Euler characteristic

Some closed hyperbolic 5-manifolds

Closed hyperbolic manifolds without spinc structures

Non-cobordant hyperbolic manifolds

Computing the twisted $L^{2}$ -Euler characteristic

Closed hyperbolic manifolds without $spin^{c}$ structures