Abstract
We express the signature modulo 4 of a closed, oriented, –dimensional manifold as a linear combination of its Euler characteristic and the new absolute torsion invariant defined by Korzeniewski [Absolute Whitehead torsion, Geom. Topol. 11 (2007) 215–249]. Let be a fibre bundle, where , and are closed, connected, and compatibly oriented manifolds. We give a formula for the absolute torsion of the total space in terms of the absolute torsion of the base and fibre, and then combine these two results to prove that the signature of is congruent modulo 4 to the product of the signatures of and .
Citation
Ian Hambleton. Andrew Korzeniewski. Andrew Ranicki. "The signature of a fibre bundle is multiplicative mod 4." Geom. Topol. 11 (1) 251 - 314, 2007. https://doi.org/10.2140/gt.2007.11.251
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