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Relevant bibliographies by topics / Seifert manifold

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Journal articles

Academic literature on the topic 'Seifert manifold'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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Journal articles on the topic "Seifert manifold"

1

Ikeda, Toru. "Essential Surfaces in Graph Link Exteriors." Canadian Mathematical Bulletin 52, no. 2 (2009): 257–66. http://dx.doi.org/10.4153/cmb-2009-028-9.

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AbstractAn irreducible graph manifold M contains an essential torus if it is not a special Seifert manifold. WhetherM contains a closed essential surface of negative Euler characteristic or not depends on the difference of Seifert fibrations from the two sides of a torus system which splits M into Seifert manifolds. However, it is not easy to characterize geometrically the class of irreducible graph manifolds which contain such surfaces. This article studies this problem in the case of graph link exteriors.

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2

Silver, Daniel S. "Examples of 3-knots with no minimal Seifert manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 3 (1991): 417–20. http://dx.doi.org/10.1017/s0305004100070481.

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We work throughout in the smooth category. Homomorphisms of fundamental and homology groups are induced by inclusion. Ann-knot, formn≥ 1, is an embeddedn-sphereK⊂Sn+2. ASeifert manifoldforKis a compact, connected, orientable (n+ 1)-manifoldV⊂Sn+2with boundary ∂V=K. By [9] Seifert manifolds always exist. As in [9] letYdenoteSn+2split alongV; Yis a compact manifold with ∂Y=V0∪V1, whereVt≈V. We say thatVis aminimal Seifert manifoldforKif π1Vt→ π1Yis a monomorphism fort= 0, 1. (Here and throughout basepoint considerations are suppressed.)

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3

COFFEY, JAMES. "THE UNIVERSAL COVER OF 3-MANIFOLDS BUILT FROM INJECTIVE HANDLEBODIES IS ℝ3". Journal of Knot Theory and Its Ramifications 17, № 10 (2008): 1257–80. http://dx.doi.org/10.1142/s0218216508006579.

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This paper gives a proof that the universal cover of a closed 3-manifold built from three π1-injective handlebodies is homeomorphic to ℝ3. This construction is an extension to handlebodies of the conditions for gluing of three solid tori to produce non-Haken Seifert fibered manifolds with infinite fundamental group. This class of manifolds has been shown to contain non-Haken non-Seifert fibered manifolds.

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4

NISHI, HARUKO. "SU(n)-CHERN–SIMONS INVARIANTS OF SEIFERT FIBERED 3-MANIFOLDS." International Journal of Mathematics 09, no. 03 (1998): 295–330. http://dx.doi.org/10.1142/s0129167x98000130.

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We derive the formula for the Chern–Simons invariants of irrreducible SU(n)-flat connections on the Seifert fibered 3-manifolds. As an example, we calculate the values explicitly for the Seifert fibered 3-manifold S3/Γ, where Γ is a finite subgroup of SU(2).

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5

Silver, Daniel S. "On the existence of minimal Seifert manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 114, no. 1 (1993): 103–9. http://dx.doi.org/10.1017/s0305004100071449.

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AbstractFor n ≥ 3, an n-knot K has a minimal Seifert manifold if and only if its group is isomorphic to an HNN-extension with finitely presented base. In this case, any Seifert manifold for K can be converted to a minimal Seifert manifold for K by some finite sequence of ambient 0- and 1-surgeries.

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6

BRITTENHAM, MARK. "ESSENTIAL LAMINATIONS, EXCEPTIONAL SEIFERT-FIBERED SPACES, AND DEHN FILLING." Journal of Knot Theory and Its Ramifications 07, no. 04 (1998): 425–32. http://dx.doi.org/10.1142/s021821659800022x.

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We show how essential laminations can be used to provide an improvement on (some of) the results of the 2π-Theorem; at most 20 Dehn fillings on a hyperbolic 3-manifold with boundary a torus T can yield a reducible manifold, finite π1 manifold, or exceptional Seifert-fibered space. Recent work of Wu allows us to add toroidal manifolds to this list, as well.

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7

Heil, Wolfgang, and Wilbur Whitten. "The Seifert Fiber Space Conjecture and Torus Theorem for Nonorientable 3-Manifolds." Canadian Mathematical Bulletin 37, no. 4 (1994): 482–89. http://dx.doi.org/10.4153/cmb-1994-070-7.

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AbstractThe Seifert-fiber-space conjecture for nonorientable 3-manifolds states that if M denotes a compact, irreducible, nonorientable 3-manifold that is not a fake P2 x S1, if π1M is infinite and does not contain Z2 * Z2 as a subgroup, and if π1M does however contain a nontrivial, cyclic, normal subgroup, then M is a Seifert bundle. In this paper, we construct all compact, irreducible, nonorientable 3-manifolds (that do not contain a fake P2 × I) each of whose fundamental group contains Z2 * Z2 and an infinité cyclic, normal subgroup; none of these manifolds admits a Seifert fibration, but they satisfy Thurston's Geometrization Conjecture. We then reformulate the statement of the (nonorientable) SFS-conjecture and obtain a torus theorem for nonorientable manifolds.

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8

Millett, Kenneth, and Dale Rolfsen. "A theorem of Borsuk—Ulam type for Seifert-fibred 3-manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 100, no. 3 (1986): 523–32. http://dx.doi.org/10.1017/s0305004100066251.

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Let M denote a compact topological 3-manifold, without boundary, foliated by topological circles in the sense of Seifert's gefaserter Räume[8]. This will be called a Seifert structure, or Seifert fibration on M; the leaves of the foliation are called (regular or exceptional) fibres. Our main result is the following theorem, reminiscent of the theorem of Borsuk—Ulam [1] stating that every continuous function from S3 to S2 takes at least one pair of antipodal points to the same value.

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9

Peet, Benjamin. "Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds." Annales Mathematicae Silesianae 33, no. 1 (2019): 235–65. http://dx.doi.org/10.2478/amsil-2019-0007.

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AbstractIn this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on the obstruction class of the Seifert manifold, it can be derived from the given construction. The obstruction condition is refined and the general structure of the finite groups that act via the construction is provided.

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10

Kropholler, P. H. "A note on centrality in 3-manifold groups." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 2 (1990): 261–66. http://dx.doi.org/10.1017/s0305004100068523.

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Centralizers in fundamental groups of 3-manifolds are well understood because of their relationship with Seifert fibre spaces. Jaco and Shalen's book [4] provides detailed information about Seifert fibre spaces in 3-manifolds, and consequently about centralizers in their fundamental groups. It is the purpose of this note to record two group-theoretic properties, both easily deduced from results of Jaco and Shalen. Doubtless many other authors could have established the same results had they needed them. Our motivation for writing this paper is that these properties can be used as a basis for group-theoretic proofs of certain fundamental results in 3-manifold theory: Proposition 1 below can be used as a basis for a proof of the Torus Theorem (cf. [8]) and Proposition 2 for the Torus Decomposition Theorem (cf. [9]).

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