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 language | English (US) |
|---|---|
| Article number | 1350048 |
| Journal | International Journal of Mathematics |
| Volume | 24 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2013 |
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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 journal › Article
}
TY - JOUR
T1 - Character varieties of once-punctured torus bundles with tunnel number one
AU - Baker, Kenneth
AU - Petersen, Kathleen L.
PY - 2013/6
Y1 - 2013/6
N2 - 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).
AB - 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).
KW - Character variety
KW - punctured torus bundle
KW - tunnel number one
UR - http://www.scopus.com/inward/record.url?scp=84879810604&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84879810604&partnerID=8YFLogxK
U2 - 10.1142/S0129167X13500481
DO - 10.1142/S0129167X13500481
M3 - Article
VL - 24
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 6
M1 - 1350048
ER -