Acylindrical surfaces and branched surfaces. I (Q1396306)

It is shown that in a compact orientable 3-manifold there are, up to isotopy, only finitely many acylindrical (the complement contains no essential annuli) or, more generally, pseudo-acylindrical incompressible surfaces (for example, totally geodesic surfaces in hyperbolic 3-manifolds are acylindrical). Similar results were obtained by \textit{J. Hass} [Mich. Math. J. 42, 357-365 (1995; Zbl 0862.57011)] and \textit{Z. Sela} [Invent. Math. 129, 527-565 (1997; Zbl 0887.20017)]; in the present paper, techniques of branched surface theory are used, and in particular results by \textit{W. Floyd} and \textit{U. Oertel} [Topology 23, 117-125 (1984; Zbl 0524.57008)].