The link volumes of some prism manifolds
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1649-1665
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We calculate the link volume of an infinite family of prism manifolds. As a corollary, we show that the link volume is not finite-to-one.

DOI : 10.2140/agt.2012.12.1649
Classification : 57M27, 57M25, 57M12
Keywords: link volume, branched coverings, Seifert manifolds

Remigio-Juárez, Jair  1   ; Rieck, Yo’av  2

1 División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco,, Km. 1 Carr. Cunduacán-Jalpa de Méndez, Cunduacán, Tab. 86690, Mexico
2 Department of Mathematical Sciences, University of Arkansas,, 301 SCEN, Fayetteville, AR 72701, USA
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Remigio-Juárez, Jair; Rieck, Yo’av. The link volumes of some prism manifolds. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1649-1665. doi: 10.2140/agt.2012.12.1649

[1] I Agol, The minimal volume orientable hyperbolic $2$–cusped $3$–manifolds, Proc. Amer. Math. Soc. 138 (2010) 3723

[2] R Benedetti, C Petronio, Lectures on hyperbolic geometry, Universitext, Springer (1992)

[3] C Cao, G R Meyerhoff, The orientable cusped hyperbolic $3$–manifolds of minimum volume, Invent. Math. 146 (2001) 451

[4] A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988)

[5] R H Fox, A quick trip through knot theory, from: "Topology of $3$–manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961)" (editor D Silver), Prentice-Hall (1962) 120

[6] C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371

[7] J Hempel, $3$–Manifolds, AMS Chelsea Publishing, Providence, RI (2004)

[8] W Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Math. 43, Amer. Math. Soc. (1980)

[9] T Kobayashi, Y Rieck, A linear bound on the tetrahedral number of manifolds of bounded volume (after J\o rgensen and Thurston), from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 27

[10] J M Montesinos, Seifert manifolds that are ramified two–sheeted cyclic coverings, Bol. Soc. Mat. Mexicana 18 (1973) 1

[11] J M Montesinos, Classical tessellations and three-manifolds, Universitext, Springer (1987)

[12] P Orlik, Seifert manifolds, Lecture Notes in Math. 291, Springer (1972)

[13] Y Rieck, Y Yamashita, The link volume of $3$–manifolds

[14] P Scott, The geometries of $3$–manifolds, Bull. London Math. Soc. 15 (1983) 401

[15] H Seifert, Topologie Dreidimensionaler Gefaserter Räume, Acta Math. 60 (1933) 147

[16] W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)

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