Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 59, Number 2 (2007), 351-370.
Mapping tori with first Betti number at least two
We show that given a finitely presented group with which is a mapping torus for a finitely generated group and an automorphism of then if the Alexander polynomial of is non-constant, we can take to be arbitrarily large. We give a range of applications and examples, such as any group with that is -by- for the non-abelian free group of rank is also -by- for infinitely many . We also examine 3-manifold groups where we show that a finitely generated subgroup cannot be conjugate to a proper subgroup of itself.
J. Math. Soc. Japan, Volume 59, Number 2 (2007), 351-370.
First available in Project Euclid: 1 October 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M05: Fundamental group, presentations, free differential calculus
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 57N10: Topology of general 3-manifolds [See also 57Mxx]
BUTTON, Jack O. Mapping tori with first Betti number at least two. J. Math. Soc. Japan 59 (2007), no. 2, 351--370. doi:10.2969/jmsj/05920351. https://projecteuclid.org/euclid.jmsj/1191247591