Celebratio Mathematica — Ranicki

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Works connected to Andrew Korzeniewski

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I. Hambleton, A. Korzeniewski, and A. Ranicki: “The signature of a fibre bundle is multiplicative \( \mod 4 \),” Geom. Topol. 11 : 1 (2007), pp. 251–314. MR 2302493 Zbl 1136.55013 ArXiv math/0502353 article

We express the signature modulo 4 of a closed, oriented, \( 4k \)-dimensional \( PL \) 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 \( F \to E \to B \) be a \( PL \) fibre bundle, where \( F \), \( E \) and \( B \) are closed, connected, and compatibly oriented \( PL \) manifolds. We give a formula for the absolute torsion of the total space \( E \) in terms of the absolute torsion of the base and fibre, and then combine these two results to prove that the signature of \( E \) is congruent modulo 4 to the product of the signatures of \( F \) and \( B \).

Andrew Korzeniewski	Related
Ian Hambleton	Related