Modifying a branched surface to carry a foliation

The Simplest Branched Surfaces for a Foliation

Given a foliation F of a closed 3-manifold and a Smale flow φ transverse to F, we associate a “simplest” branched surface with the pair (F, φ), which is unique up to two combinatorial moves. We show that all branched surfaces constructed from F and φ can be obtained from the simplest model by applying a finite sequence of these moves chosen so that each intermediate branched surface also carrie...

Smooth Maps Transverse to a Foliation

Enumerating branched orientable surface coverings over a non-orientable surface

The isomorphism classes of several types of graph coverings of a graph have been enumerated by many authors [M. Hofmeister, Graph covering projections arising from finite vector space over finite fields, Discrete Math. 143 (1995) 87–97; S. Hong, J.H. Kwak, J. Lee, Regular graph coverings whose covering transformation groups have the isomorphism extention property, Discrete Math. 148 (1996) 85–1...

Detecting When a Nonsingular Flow Is Transverse to a Foliation

We show that any foliation transverse to a C 1 nonsingular flow φ on a closed 3-manifold can be detected algorithmically. We use this to describe a procedure that, for any δ > 0, will determine whether or not there is a foliation whose tangent space is bounded away from the tangent space to φ by a distance of δ.

microleakage evaluation in regard to cavo-surface designs & treatments

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