Totally geodesic surfaces and quadratic forms

Let M be a compact, connected, irreducible, orientable 3-manifold with torus boundary. A closed, orientable, immersed, incompressible surface F in M with no incompressible annulus joining F and ∂M compresses in at most finitely many Dehn fillings M(α). It is known that there is no universal upper bo...

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Bibliographic Details
Main Author: Pradthana Jaipong
Format: Journal
Published: 2018
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84888213662&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/47520
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Institution: Chiang Mai University
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Summary:Let M be a compact, connected, irreducible, orientable 3-manifold with torus boundary. A closed, orientable, immersed, incompressible surface F in M with no incompressible annulus joining F and ∂M compresses in at most finitely many Dehn fillings M(α). It is known that there is no universal upper bound on the number of such fillings, independent of the surface, and the figure-eight knot complement is the first example of a manifold where this phenomenon occurs. In this paper, we show that the same behavior of the figure-eight knot complement is shared by other two cusped manifolds. © 2013 World Scientific Publishing Company.