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A method of constructing 3-manifolds and its application to the computation of the μ-invariant

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Hilden, Hugh Michael and Montesinos Amilibia, José María (1978) A method of constructing 3-manifolds and its application to the computation of the μ-invariant. In Algebraic and geometric topology. Proceedings of symposia in pure mathematics, 2 (32). American Mathematical Society, Providence, pp. 61-69. ISBN 0-8218-1433-8



Abstract

If F and G are disjoint compact surfaces with boundary in S3=∂D4, let F′ and G′ be the result of pushing F and G into the interior of D4, keeping ∂F and ∂G fixed. The authors give an explicit cut and paste description of an irregular 3-fold branched cover W4(F,G) of D4 branched along F∪G. If M3=∂W4(F,G), they say that (F,G) "represents M3 by bands''. Their main result is that any closed oriented 3-manifold can be so represented. In particular, any such 3-manifold bounds a simply connected W4 which is an irregular 3-fold branched cover of D4. Moreover, F and G can always be chosen in a rather special form which leads to a formula for the μ-invariant of M3 when M3 is a (Z/2)-homology sphere.


Item Type:Book Section
Additional Information:

Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society (Twenty-fourth Summer Research Institute), held at Stanford University, Stanford, Calif., August 2–21, 1976

Uncontrolled Keywords:Manifolds and cell complexes
Subjects:Sciences > Mathematics > Topology
ID Code:22036
Deposited On:21 Jun 2013 15:55
Last Modified:12 Dec 2018 15:14

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