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

TL;DR

This paper demonstrates the existence of infinitely many achiral 1-cusped hyperbolic 3-manifolds that are not derived from amphicheiral null-homologous knot complements, expanding understanding of their diversity beyond known examples.

Contribution

It proves the existence of infinitely many such manifolds that are not homeomorphic to any amphicheiral null-homologous knot complement in any closed achiral 3-manifold.

Findings

Existence of infinitely many achiral 1-cusped hyperbolic 3-manifolds not from amphicheiral knot complements

These manifolds are not homeomorphic to any amphicheiral null-homologous knot complement

Contrasts with the sporadic occurrence of achiral hyperbolic 3-manifolds among small volume cases

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.