Atlas: Transfinite central series of compact three manifold groups by Kent E. Orr

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The 1996 Joint Spring Topology Conference and Southeast Dynamical Systems Conference
March 7-9, 1996
Ball State University
Muncie, IN, USA

Organizers
John Emert, Kerry Jones, Roger Nelson

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Transfinite central series of compact three manifold groups
by
Kent E. Orr
Indiana University
Coauthors: Tim D. Cochran (Indiana University)

The length of a group G is the least ordinal \alpha such G_\alpha = G_\alpha+1 where G_\alpha is the \alpha^th term in the transfinite lower central series of G. We establish connections between the length of compact three manifold groups and various central open problems such as the Parafree conjecture, the link slice problem, and the four dimensional topological surgery conjecture. We prove prove the length of all surface groups and most Fuchsian groups is at most \omega. Similar results hold for Seifert fibered three manifold groups. Our main result is the existence of hyperbolic three manifold groups of length at least 3 \omega

Date received: February 9, 1996