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Representing elements of π1M3 by fibred knots

Published online by Cambridge University Press:  24 October 2008

John Harer
John Harer
Affiliation:
Columbia University, New York
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Extract

Every smooth, closed, orientable manifold of dimension 3 contains a fibred knot, i.e. an imbedded circle K such that M – K is the total space of a fibre bundle over S1 whose fibre F is standard near K. This means the boundary of the closure of F is K so that K is null-homologous in M. A natural problem suggested by Rolfsen (see (2), problem 3·13) is to determine which elements of π1M3 may be represented by fibred knots. We deal with this by proving the

Theorem. The collection of all elements of π1 M3 which can be represented by fibred knots is exactly the commutator subgroup [π1 M3, π1 M3].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 133 - 138
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

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