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Surgeries on periodic links and homology of periodic 3-manifolds

Published online by Cambridge University Press:  26 October 2001

JÓZEF H. PRZYTYCKI  and
MAXIM V. SOKOLOV
JÓZEF H. PRZYTYCKI
Affiliation:
Mathematics Department, George Washington University, Washington, DC 20052, U.S.A. e-mail: przytyck@research.circ.gwu.edu
MAXIM V. SOKOLOV
Affiliation:
Mathematics Department, George Washington University, Washington, DC 20052, U.S.A. e-mail: przytyck@research.circ.gwu.edu
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Abstract

Fix a prime integer p. We show that a closed orientable 3-manifold M admits an action of Zp with the fixed point set S1 if and only if M can be obtained as the result of surgery on a p-periodic framed link L and Zp acts freely on the components of L. We prove a similar theorem for free Zp-actions. As an interesting application, we prove the following, rather unexpected result: for any M as above and for any odd prime p, H1(M, Zp) ≠ Zp. We also prove a similar criterion of 2-periodicity for rational homology 3-spheres.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 2 , September 2001 , pp. 295 - 307
Copyright
2001 Cambridge Philosophical Society

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