Algebraic invariants, mutation, and commensurability of link complements

Eric Chesebro, Jason Deblois

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable, distinguished by their scissors congruence classes. Mutation produces arbitrarily large finite subfamilies of nonisometric manifolds with the same volume and scissors congruence class. Depending on the choice of mutation, these manifolds may be commensurable or incommensurable, distinguished in the latter case by cusp parameters. All have trace field ℚ(i, √2); some have integral traces while others do not.

Original languageEnglish
Pages (from-to)341-398
Number of pages58
JournalPacific Journal of Mathematics
Volume267
Issue number2
DOIs
StatePublished - 2014

Keywords

  • Bloch invariant
  • Commensurability
  • Link
  • Mutation
  • Trace field

Fingerprint

Dive into the research topics of 'Algebraic invariants, mutation, and commensurability of link complements'. Together they form a unique fingerprint.

Cite this