Abstract:Given a 3 manifold $M$ with torus boundary and an ideal triangulation, Yoshida and Tillmann give different methods to construct surfaces embedded in $M$ from ideal points of the deformation variety. Yoshida builds a surface from twisted squares, whereas Tillmann produces a spun-normal surface. We investigate the relation between the generated surfaces and extend a result of Tillmann’s (that if the ideal point of the deformation variety corresponds to an ideal point of the character variety, then the generated spun-normal surface is detected by the character variety) to the generated twisted squares surfaces.
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- Henry Segerman
- Affiliation: Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, Texas 78712-0257
- MR Author ID: 723574
- ORCID: 0000-0002-4532-3095
- Email: firstname.lastname@example.org
- Received by editor(s): October 10, 2008
- Received by editor(s) in revised form: March 7, 2009
- Published electronically: July 15, 2009
- Additional Notes: The author was partially supported by an NSF-RTG postdoctoral fellowship.
- Communicated by: Daniel Ruberman
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 137 (2009), 4259-4273
- MSC (2000): Primary 57M99
- DOI: https://doi.org/10.1090/S0002-9939-09-09960-2
- MathSciNet review: 2538587