caa a22 4500 445884509 CHVBK 20180317145555.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10711-010-9501-z doi (NATIONALLICENCE)springer-10.1007/s10711-010-9501-z Segerman Henry University of Texas at Austin, Austin, TX, USA aut Detection of incompressible surfaces in hyperbolic punctured torus bundles [Elektronische Daten] [Henry Segerman] Culler and Shalen, and later Yoshida, give ways to construct incompressible surfaces in 3-manifolds from ideal points of the character and deformation varieties, respectively. We work in the case of hyperbolic punctured torus bundles, for which the incompressible surfaces were classified by Floyd and Hatcher, and independently by Culler, Jaco and Rubinstein. We convert non fiber incompressible surfaces from their form to the form output by Yoshida's construction, and run his construction backwards to give (for non semi-fibers, which we identify) the data needed to construct ideal points of the deformation variety corresponding to those surfaces via Yoshida's construction. We use a result of Tillmann to show that the same incompressible surfaces can be obtained from an ideal point of the character variety via the Culler-Shalen construction. In particular this shows that all boundary slopes of non fiber and non semi-fiber incompressible surfaces in hyperbolic punctured torus bundles are strongly detected. Springer Science+Business Media B.V., 2010 Incompressible surfaces nationallicence Punctured torus bundles nationallicence Ideal point nationallicence Triangulation nationallicence Deformation variety nationallicence Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 181-232 0046-5755 150:1<181 2011 150 10711 https://doi.org/10.1007/s10711-010-9501-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9501-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Segerman Henry University of Texas at Austin, Austin, TX, USA aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 181-232 0046-5755 150:1<181 2011 150 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer