Achiral 1-cusped hyperbolic 3-manifolds not coming from amphicheiral null-homologous knot complements

Abstract

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.

10 pages, 9 figures

References in corpus (2)

• Symmetries of spatial graphs and Simon invariants
• Cosmetic surgery and the $SL(2,\mathbb{C})$ Casson invariant for two-bridge knots