Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On spun-normal and twisted squares surfaces
HTML articles powered by AMS MathViewer

by Henry Segerman
Proc. Amer. Math. Soc. 137 (2009), 4259-4273
DOI: https://doi.org/10.1090/S0002-9939-09-09960-2
Published electronically: July 15, 2009
PDF | 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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57M99
  • Retrieve articles in all journals with MSC (2000): 57M99
Bibliographic 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