Abstract
The torsion τ of a 3-manifold can be reformulated in terms of a “torsion function” on the set of Euler structures. It is defined in Section 1 where we also discuss basic Euler structures and gluing formulas for torsion functions and compute the torsion function for link exteriors. In Section 2 we study the moments of the torsion function. In Section 3 we develop an axiomatic approach to the torsion function. In Section 4 we give an explicit formula for the torsion function of a 3-manifold obtained by surgery on an algebraically split link in S3. More general formulas are obtained in Section 5 where we also define (in the case b1 = 1) a so-called modified torsion function.
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© 2002 Springer Basel AG
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Turaev, V. (2002). The Torsion Function. In: Torsions of 3-dimensional Manifolds. Progress in Mathematics, vol 208. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7999-6_9
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DOI: https://doi.org/10.1007/978-3-0348-7999-6_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9398-5
Online ISBN: 978-3-0348-7999-6
eBook Packages: Springer Book Archive