Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On spun-normal and twisted squares surfaces


Author: Henry Segerman
Journal: Proc. Amer. Math. Soc. 137 (2009), 4259-4273
MSC (2000): Primary 57M99
Published electronically: July 15, 2009
MathSciNet review: 2538587
Full-text PDF Free Access

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 [Enhancements On Off] (What's this?)

  • 1. Henry Segerman, Detection of incompressible surfaces in hyperbolic punctured torus bundles, arXiv:math/0610302v2.
  • 2. Peter B. Shalen, Representations of 3-manifold groups, Handbook of geometric topology, North-Holland, Amsterdam, 2002, pp. 955–1044. MR 1886685
  • 3. Stephan Tillmann, Degenerations of ideal hyperbolic triangulations, arXiv:math.GT/0508295.
  • 4. Stephan Tillmann, Normal surfaces in topologically finite 3-manifolds, Enseign. Math. (2) 54 (2008), no. 3-4, 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, 10.1016/0040-9383(91)90003-M

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57M99

Retrieve articles in all journals with MSC (2000): 57M99


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: http://dx.doi.org/10.1090/S0002-9939-09-09960-2
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.