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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On spun-normal and twisted squares surfaces
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by Henry Segerman PDF
Proc. Amer. Math. Soc. 137 (2009), 4259-4273 Request permission

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
  • Henry Segerman, Detection of incompressible surfaces in hyperbolic punctured torus bundles, arXiv:math/0610302v2 .
  • Peter B. Shalen, Representations of 3-manifold groups, Handbook of geometric topology, North-Holland, Amsterdam, 2002, pp. 955–1044. MR 1886685
  • Stephan Tillmann, Degenerations of ideal hyperbolic triangulations, arXiv:math.GT/0508295 .
  • Stephan Tillmann, Normal surfaces in topologically finite 3-manifolds, Enseign. Math. (2) 54 (2008), no. 3-4, 329–380. MR 2478091
  • Genevieve S. Walsh, Incompressible surfaces and spunnormal form, arXiv:math/0503027 .
  • Tomoyoshi Yoshida, On ideal points of deformation curves of hyperbolic $3$-manifolds with one cusp, Topology 30 (1991), no. 2, 155–170. MR 1098911, DOI 10.1016/0040-9383(91)90003-M
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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
  • MR Author ID: 723574
  • ORCID: 0000-0002-4532-3095
  • Email: henrys@math.utexas.edu
  • 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