Abstract
In this chapter we generalize Theorem VII.2.2 to arbitrary links in homology spheres. We begin with key technical Lemmas 1.2 and 1.4. Lemma 1.2 will be used in the proof of Lemma 1.4 and in Section 5. Lemma 1.4 will be used in Section 2 where we establish a general surgery formula for φ-torsions. As a special case we obtain in Section 3 a surgery formula for the Alexander polynomial. In Section 4 we establish a surgery formula for the torsion τ. In Section 5 we consider the realization problem for τ. The exposition in Section 5 uses Lemma 1.2 but otherwise is independent of the rest of the chapter.
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© 2002 Springer Basel AG
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Turaev, V. (2002). Surgery Formulas for Torsions. In: Torsions of 3-dimensional Manifolds. Progress in Mathematics, vol 208. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7999-6_8
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DOI: https://doi.org/10.1007/978-3-0348-7999-6_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9398-5
Online ISBN: 978-3-0348-7999-6
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