Cyclic and finite surgeries on pretzel knots

Sangyop Lee; Seungsang Oh; Masakazu Teragaito

doi:10.1142/S0218216502002037

Cyclic and finite surgeries on pretzel knots

Sangyop Lee, Seungsang Oh, Masakazu Teragaito

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

4 Citations (Scopus)

Abstract

We classify Dehn surgeries on (p, q, r) pretzel knots resulting in a manifold M(α) having cyclic fundamental group and analyze those leading to a finite fundamental group. The proof uses the theory of cyclic and finite surgeries developed by Culler, Shalen, Boyer, and Zhang. In particular, Culler-Shalen seminorms play a central role.

Original language	English
Pages (from-to)	891-902
Number of pages	12
Journal	Journal of Knot Theory and its Ramifications
Volume	11
Issue number	6
DOIs	https://doi.org/10.1142/S0218216502002037
Publication status	Published - 2002 Sept
Externally published	Yes

Keywords

Character variety
Culler-Shalen seminorms
Dehn surgery
Exceptional surgery
Pretzel knot

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216502002037

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abstract = "We classify Dehn surgeries on (p, q, r) pretzel knots resulting in a manifold M(α) having cyclic fundamental group and analyze those leading to a finite fundamental group. The proof uses the theory of cyclic and finite surgeries developed by Culler, Shalen, Boyer, and Zhang. In particular, Culler-Shalen seminorms play a central role.",

keywords = "Character variety, Culler-Shalen seminorms, Dehn surgery, Exceptional surgery, Pretzel knot",

author = "Sangyop Lee and Seungsang Oh and Masakazu Teragaito",

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AU - Lee, Sangyop

AU - Oh, Seungsang

AU - Teragaito, Masakazu

N1 - Funding Information: This research was supported by grants NSERC OGP 0009446 and FCAR EQ 3518.

PY - 2002/9

Y1 - 2002/9

N2 - We classify Dehn surgeries on (p, q, r) pretzel knots resulting in a manifold M(α) having cyclic fundamental group and analyze those leading to a finite fundamental group. The proof uses the theory of cyclic and finite surgeries developed by Culler, Shalen, Boyer, and Zhang. In particular, Culler-Shalen seminorms play a central role.

AB - We classify Dehn surgeries on (p, q, r) pretzel knots resulting in a manifold M(α) having cyclic fundamental group and analyze those leading to a finite fundamental group. The proof uses the theory of cyclic and finite surgeries developed by Culler, Shalen, Boyer, and Zhang. In particular, Culler-Shalen seminorms play a central role.

KW - Character variety

KW - Culler-Shalen seminorms

KW - Dehn surgery

KW - Exceptional surgery

KW - Pretzel knot

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DO - 10.1142/S0218216502002037

M3 - Article

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ER -

Cyclic and finite surgeries on pretzel knots

Abstract

Keywords

ASJC Scopus subject areas

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