Cosmetic surgery and the link volume of hyperbolic 3–manifolds

Rieck, Yo’av¹ ; Yamashita, Yasushi²

¹Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, United States
²Department of Information and Computer Sciences, Nara Women’s University Kitauoya, Nishimachi, Nara 630-0586, Japan

Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3445-3521

Résumé

We prove that for any V > 0 there exists a hyperbolic manifold MV such that Vol(MV ) < 2.03 and LinkVol(MV ) > V . This was conjectured by the authors in [Algebr. Geom. Topol. 13 (2013) 927–958, Conjecture 1.3].

The proof requires study of cosmetic surgery on links (equivalently, fillings of manifolds with boundary tori). There is no bound on the number of components of the link (or boundary components). For statements, see the second part of the introduction. Here are two examples of the results we obtain:

Détail

DOI : 10.2140/agt.2016.16.3445

Classification : 57M12, 57M50
Keywords: link volume, hyperbolic volume, cosmetic surgery, Dehn surgery, 3–manifolds, hyperbolic manifolds, branched covering

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