Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Finitely generated Kleinian groups in $ 3$-space and $ 3$-manifolds of infinite homotopy type


Author: L. Potyagaĭlo
Journal: Trans. Amer. Math. Soc. 344 (1994), 57-77
MSC: Primary 57M50; Secondary 20H10, 30F40, 57N10, 57S30
MathSciNet review: 1250823
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the existence of a finitely generated Kleinian group $ N \subset S{O_ + }(1,4)$ acting freely on an invariant component $ \Omega \subset {S^3}$ without parabolic elements such that the fundamental group $ {\pi _1}(\Omega /N)$ is not finitely generated.

Moreover, N is a finite index subgroup of a Kleinian group $ {N_0}$ which has infinitely many conjugacy classes of elliptic elements.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M50, 20H10, 30F40, 57N10, 57S30

Retrieve articles in all journals with MSC: 57M50, 20H10, 30F40, 57N10, 57S30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1250823-6
PII: S 0002-9947(1994)1250823-6
Keywords: Kleinian groups, conformal group of euclidean space, uniformization of 3-manifolds, surface bundle over the circle
Article copyright: © Copyright 1994 American Mathematical Society