Links and spines

Yuya Koda

doi:10.1142/S0218216511009674

Links and spines

Yuya Koda

Research output: Contribution to journal › Article › peer-review

Abstract

We define two kinds of invariants of links in closed 3-manifolds, the s-complexity (s ∈ ℕ) and the block number, by considering decompositions of links in closed orientable 3-manifolds by spines. The first one is a generalization of the complexity of links defined by Pervova and Petronio. After providing properties of these invariants, we construct special spines of strongly-cyclic coverings branched over generalized twist knots in lens spaces, including S ³ and ℝP ³, which provide upper bounds for the invariants.

Original language	English
Article number	1250027
Journal	Journal of Knot Theory and its Ramifications
Volume	21
Issue number	3
DOIs	https://doi.org/10.1142/S0218216511009674
Publication status	Published - 2012 Mar
Externally published	Yes

Keywords

3-manifold
complexity
Knot
link
spine

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216511009674

Cite this

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title = "Links and spines",

abstract = "We define two kinds of invariants of links in closed 3-manifolds, the s-complexity (s ∈ ℕ) and the block number, by considering decompositions of links in closed orientable 3-manifolds by spines. The first one is a generalization of the complexity of links defined by Pervova and Petronio. After providing properties of these invariants, we construct special spines of strongly-cyclic coverings branched over generalized twist knots in lens spaces, including S 3 and ℝP 3, which provide upper bounds for the invariants.",

keywords = "3-manifold, complexity, Knot, link, spine",

author = "Yuya Koda",

note = "Funding Information: The author would like to express his sincere gratitude to Sergei Matveev for his very helpful comments to improve the exposition and for pointing out the simple proofs of Lemmas 1.2 and 1.3. He would like to thank Andrew Gibson for several useful comments, corrections and suggestions for improvement. He is also grateful to the anonymous referee for carefully reading the paper and suggesting many improvements. Part of this work was done while the author was supported in part by JSPS Global COE program “Computationism as a Foundation for the Sciences”. He is also supported by Grant-in-Aid for Young Scientists (B) 20525167.",

year = "2012",

month = mar,

doi = "10.1142/S0218216511009674",

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volume = "21",

journal = "Journal of Knot Theory and its Ramifications",

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N1 - Funding Information: The author would like to express his sincere gratitude to Sergei Matveev for his very helpful comments to improve the exposition and for pointing out the simple proofs of Lemmas 1.2 and 1.3. He would like to thank Andrew Gibson for several useful comments, corrections and suggestions for improvement. He is also grateful to the anonymous referee for carefully reading the paper and suggesting many improvements. Part of this work was done while the author was supported in part by JSPS Global COE program “Computationism as a Foundation for the Sciences”. He is also supported by Grant-in-Aid for Young Scientists (B) 20525167.

PY - 2012/3

Y1 - 2012/3

N2 - We define two kinds of invariants of links in closed 3-manifolds, the s-complexity (s ∈ ℕ) and the block number, by considering decompositions of links in closed orientable 3-manifolds by spines. The first one is a generalization of the complexity of links defined by Pervova and Petronio. After providing properties of these invariants, we construct special spines of strongly-cyclic coverings branched over generalized twist knots in lens spaces, including S 3 and ℝP 3, which provide upper bounds for the invariants.

AB - We define two kinds of invariants of links in closed 3-manifolds, the s-complexity (s ∈ ℕ) and the block number, by considering decompositions of links in closed orientable 3-manifolds by spines. The first one is a generalization of the complexity of links defined by Pervova and Petronio. After providing properties of these invariants, we construct special spines of strongly-cyclic coverings branched over generalized twist knots in lens spaces, including S 3 and ℝP 3, which provide upper bounds for the invariants.

KW - 3-manifold

KW - complexity

KW - Knot

KW - link

KW - spine

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ER -

Links and spines

Abstract

Keywords

ASJC Scopus subject areas

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