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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

On spun-normal and twisted squares surfaces

Author(s): Henry Segerman
Journal: Proc. Amer. Math. Soc. 137 (2009), 4259-4273.
MSC (2000): Primary 57M99
Posted: July 15, 2009
MathSciNet review: 2538587
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Abstract | References | Similar articles | Additional information

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.

References:

1.
Henry Segerman, Detection of incompressible surfaces in hyperbolic punctured torus bundles, arXiv:math/0610302v2.

2.
Peter Shalen, Representations of $ 3$-manifold groups, Handbook of Geometric Topology (R.B. Sher and R.J. Daverman, eds.), North-Holland, first ed., 2001. MR 1886685 (2003d:57002)

3.
Stephan Tillmann, Degenerations of ideal hyperbolic triangulations, arXiv:math.GT/0508295.

4.
-, Normal surfaces in topologically finite $ 3$-manifolds, L'Enseignement Mathématique 54 (2008), 329-380.

MR 2478091

5.
Genevieve S. Walsh, Incompressible surfaces and spunnormal form, arXiv:math/0503027.

6.
Tomoyoshi Yoshida, On ideal points of deformation curves of hyperbolic $ 3$-manifolds with one cusp, Topology 30 (1991), no. 2, 155-170. MR 1098911 (92a:57018)

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Additional Information:

Henry Segerman
Affiliation: Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, Texas 78712-0257
Email: henrys@math.utexas.edu

DOI: 10.1090/S0002-9939-09-09960-2
PII: S 0002-9939(09)09960-2
Received by editor(s): October 10, 2008,
Received by editor(s) in revised form: March 7, 2009
Posted: July 15, 2009
Additional Notes: The author was partially supported by an NSF-RTG postdoctoral fellowship.
Communicated by: Daniel Ruberman
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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