Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1353–1361 | Cite as

Achiral 1-Cusped Hyperbolic 3-Manifolds Not Coming from Amphicheiral Null-homologous Knot Complements

  • K. IchiharaEmail author
  • I. D. Jong
  • K. Taniyama
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev


It is experimentally known that achiral hyperbolic 3-manifolds are quite sporadic at least among those with small volume, while we can find plenty of them as amphicheiral knot complements in the 3-sphere. In this paper, we show that there exist infinitely many achiral 1-cusped hyperbolic 3- manifolds not homeomorphic to any amphicheiral null-homologous knot complement in any closed achiral 3-manifold.

Keywords and phrases

Amphicheiral knot banding achiral hyperbolic 3-manifold chirally cosmetic filling chirally cosmetic surgery 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of Humanities and SciencesNihon UniversitySetagaya-ku, TokyoJapan
  2. 2.Department of MathematicsKindai UniversityHigashiosaka City, OsakaJapan
  3. 3.Department of Mathematics, School of EducationWaseda UniversityShinjuku-ku, TokyoJapan

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