Abstract
Throughout this chapter, M is an oriented three-dimensional ℚ-homology sphere and H = H1(M). In Section 1 we compute the first elementary ideal of π1(M) from τ(M). In Section 2 we compute the linking form of M from τ(M) and discuss quadratic functions on H. In Section 3 we discuss relationships between τ(M) and the cohomology rings H*(M; ℤ r ) with r ≥ 2. In Section 4 we give a gluing formula for τ(M) similar to Theorem VII.1.4. In Section 5 we give a surgery formula for τ(M) similar to Theorem VIII.4.2. In Section 6 we discuss the torsion function of M.
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© 2002 Springer Basel AG
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Turaev, V. (2002). Torsion of Rational Homology Spheres. In: Torsions of 3-dimensional Manifolds. Progress in Mathematics, vol 208. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7999-6_10
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DOI: https://doi.org/10.1007/978-3-0348-7999-6_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9398-5
Online ISBN: 978-3-0348-7999-6
eBook Packages: Springer Book Archive