Generalized Chen–Yang volume conjecture for 3-manifolds

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Let MM be a compact orientable 3-manifold with empty or toroidal boundary. Define

LTV(M):=lim sup⁡r→∞, r odd⁡2πrlog⁡∣TVr(M)∣,LTV(M):=\limsup_{r\rightarrow\infty,\ r\ \operatorname{odd}}\frac{2\pi}{r}\log\lvert TV_r(M)\rvert,

where rr runs over all odd integers, and let Vol⁡(M)\operatorname{Vol}(M) be the simplicial volume, equivalently the sum of the volumes of the hyperbolic pieces in the geometric decomposition of MM. The generalized Chen–Yang volume conjecture.

LTV(M)=Vol⁡(M).LTV(M)=\operatorname{Vol}(M).

This conjecture extends the finite-volume hyperbolic case to all compact orientable 3-manifolds with empty or toroidal boundary, using the geometric decomposition into hyperbolic and Seifert-fibered pieces. The source gives no resolution of the general statement.

References

Primary source

Renaud Detcherry, Efstratia Kalfagianni and Shashini Marasinghe, “Seifert cobordisms and the Chen-Yang volume conjecture”, arXiv:2505.01546 (2025).

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