Hyperbolic 3-Manifolds that Fiber over the Circle
📜 Abstract
This paper studies the geometry of hyperbolic 3-manifolds which fiber over the circle, with the fibers being surfaces with punctures. It is shown that the complete hyperbolic structure on these manifolds can be described by a simple canonical ideal triangulation.
✨ Summary
The paper “Hyperbolic 3-Manifolds that Fiber over the Circle” by S. A. Bleiler and C. D. Hodgson published in 1996 delves into the geometric structures of hyperbolic 3-manifolds that fiber over the circle, particularly focusing on manifolds where the fibers are punctured surfaces. The key contributions of this work include demonstrating that such manifolds can be characterized by complete hyperbolic structures and described via simple canonical ideal triangulations.
A quick web search reveals that this paper has had limited direct influence on subsequent publications or industry applications. It serves primarily as a foundation in complex geometric studies related to hyperbolic manifolds and has implications in the broader field of geometric topology. This paper is often referenced in academic contexts where deep mathematical and topological properties of manifolds are studied; however, it has not led to significant applied or transformative uses outside this specific area of academic research.