Taut Foliations and ℝ‐Covered Foliations With Transverse Measure on 3‐Manifolds

Key Points

• To establish conditions under which a taut foliation on closed 3-manifolds relates to fibration and ℝ-coveredness.
• Establishment of a theorem for taut foliations on closed 3-manifolds.
• Analysis of conditions for monotone equivalence and perturbation of fibrations.
• Provided sufficient conditions for taut foliation perturbing into a fibration.
• Identified circumstances under which a taut foliation qualifies as ℝ-covered.