Hyperbolic 4-manifolds with perfect circle-valued Morse functions
Hyperbolic 4-manifolds with perfect circle-valued Morse functions
We exhibit some (compact and cusped) finite-volume hyperbolic four-manifolds M with perfect circle-valued Morse functions, that is circlevalued Morse functions f : M → 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 …