Hyperbolic 4-manifolds with perfect circle-valued Morse functions.

We exhibit some (compact and cusped) finite-volume hyperbolic 4-manifolds M with perfect circle-valued Morse functions, that is circle-valued Morse functions f\colon M \to S^1 with only index 2 critical points. We construct in particular one example where every generic circle-valued function is homotopic to a perfect one. An immediate consequence is the existence of infinitely many finite-volume (compact and cusped) hyperbolic 4-manifolds M having a handle decomposition with bounded numbers of 1- and 3-handles, so with bounded Betti numbers b_1(M), b_3(M) and rank \mathrm {rk}(\pi _1(M)). [ABSTRACT FROM AUTHOR]