On spun-normal and twisted squares surfaces

Details On spun-normal and twisted squares surfaces On spun-normal and twisted squares surfaces

2008-10-07

arxiv.org/abs/0810.1256v1

Proc.Amer.Math.Soc. 137 (2009), 4259-4273

Mathematics

Geometric Topology

14 pages, 10 figures

Scientific paper

10.1090/S0002-9939-09-09960-2

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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