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- Title
Trace fields of representations and virtually Haken 3-manifolds.
- Authors
XINGRU ZHANG
- Abstract
We introduce and study trace fields and invariant trace fields of SL2(C) and PSL2(C) representations of 3-manifold groups. We give conditions on such fields which imply that the underlying 3-manifold is virtually Haken or has virtually positive or ∞ first Betti number. In particular, we define the notion of an algebraically trace-proper surface subgroup in a 3-manifold group, and show that any closed orientable irreducible 3-manifold with such a surface subgroup is virtually Haken. We give infinitely many families of closed orientable hyperbolic non-Haken 3-manifolds with algebraically trace-proper surface subgroups.
- Subjects
INVARIANTS (Mathematics); INFINITE-dimensional manifolds; PRODUCTS of subgroups; ALGEBRAIC surfaces; ALGEBRA
- Publication
Quarterly Journal of Mathematics, 2005, Vol 56, Issue 3, p431
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hah041