Seifert Manifolds

Orlik, Peter

doi:10.1007/bfb0060329

Cited by 347 publications

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“…A Seifert invariant (α, β) determines a filling in which αq + βt becomes contractible, where q is the cross-section and t is the fiber. So the surgery coefficients of our link produce one exceptional fiber with Seifert invariant (n, 1 − n) for each L i , and one with Seifert invariants (n, gn − 1) for L. In the notation of [8], the unnormalized Seifert invariants of Y are {0; (o 1 , 0); (n, 1 − n), . .…”

Section: Proof Of Theoremmentioning

confidence: 99%

Imbeddings of free actions on handlebodies

McCullough

2002

Proc. Amer. Math. Soc.

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Abstract. Fix a free, orientation-preserving action of a finite group G on a 3-dimensional handlebody V . Whenever G acts freely preserving orientation on a connected 3-manifold X, there is a G-equivariant imbedding of V into X. There are choices of X closed and Seifert-fibered for which the image of V is a handlebody of a Heegaard splitting of X. Provided that the genus of V is at least 2, there are similar choices with X closed and hyperbolic.

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Section: Proof Of Theoremmentioning

confidence: 99%

Imbeddings of free actions on handlebodies

McCullough

2002

Proc. Amer. Math. Soc.

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“…As general references on branched coverings see [1], [2], [10], [14], and [15]. For basic definitions and results on Seifert 3-manifolds we refer to [12], [15], [16] and [19].…”

Section: G R = (V(g)c~1(r))mentioning

confidence: 99%

Crystallizations of Seifert Fibered 3-Manifolds

Ruini¹

1998

Demonstratio Mathematica

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We study a class of Seifert fibered 3-manifolds M (g,n), depending on two non-negative integers, which arise from polyhedral schemata. Then we completely determine their Seifert invariants by using the crystallization theory, i.e. a representation of closed connected triangulated manifolds by edge-colored graphs. We also obtain a geometric presentation of the fundamental group 7Ti(M(g,n)) corresponding to a spine of M(g,n). Finally we show that M(g, 1) is a 2-fold covering of S 3 branched over a special 3-bridge link. Introduction and notationThroughout this paper we work in the piecewise-linear (PL) category in the sense of [18]. If A" is a finite collection of closed balls, we set \K\ = U{A : A G K}. Then K is said to be a pseudocomplex if and only if 1) \K\ = disjoint U{A : A e K}; 2) If A, B 6 K, then A n B is a union of balls of K; 3) For each /i-ball A £ K, the poset {B 6 K : B C A}, ordered by inclusion, is isomorphic with the lattice of all faces of the standard /i-simplex. The dimension of a pseudocomplex K is defined as max{dim A : A 6 K}. By abuse of language we call simplexes the balls of K and denote by S r (K) the set of all r-simplexes of K. A n-dimensional pseudocomplex K is said to be contracted if the set of its O-simplexes has cardinality n + 1. A pseu-

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“…Let a pair (ft, v f .) be the invariant uniquely determined for each exceptional orbit SO(3)/Z^ ( [5], [10]). The purpose of this section is to prove Theorem 1 (where g is the genus of M*).…”

Section: G Acts On a Locally Compact Space M And Assume That All Orbmentioning

confidence: 99%

Classification of $SO(3)$-Actions on Five Manifolds

Nakanishi¹

1978

Publ. Res. Inst. Math. Sci.

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Seifert Manifolds

Cited by 347 publications

References 0 publications

Imbeddings of free actions on handlebodies

Imbeddings of free actions on handlebodies

Crystallizations of Seifert Fibered 3-Manifolds

Classification of $SO(3)$-Actions on Five Manifolds

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