Character varieties of once-punctured torus bundles with tunnel number one

Kenneth Baker, Kathleen L. Petersen

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We determine the PSL2(&complexes) and SL2(& complexes) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling one boundary component of the Whitehead link exterior. In particular, we determine natural models for these algebraic sets, identify them up to birational equivalence with smooth models, and compute the genera of the canonical components. This enables us to compare dilatations of the monodromies of these bundles with these genera. We also determine the minimal polynomials for the trace fields of these manifolds. Additionally, we study the action of the symmetries of these manifolds upon their character varieties, identify the characters of their lens space fillings, and compute the twisted Alexander polynomials for their representations to SL2(ℂ).

Original languageEnglish (US)
Article number1350048
JournalInternational Journal of Mathematics
Volume24
Issue number6
DOIs
StatePublished - Jun 2013

Fingerprint

Character Variety
Tunnel
Bundle
Torus
Genus
Algebraic Set
Lens Space
Alexander Polynomial
Minimal polynomial
Dilatation
Trace
Equivalence
Symmetry
Model

Keywords

  • Character variety
  • punctured torus bundle
  • tunnel number one

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Character varieties of once-punctured torus bundles with tunnel number one. / Baker, Kenneth; Petersen, Kathleen L.

In: International Journal of Mathematics, Vol. 24, No. 6, 1350048, 06.2013.

Research output: Contribution to journalArticle

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