arXiv math/05023492005-02-16math.ATmath.GT

Absolute Whitehead torsion

Andrew Korzeniewski

备注：: To appear in the MPI preprint series
发表信息：: Geom. Topol. 11 (2007) 215-249
DOI：: 10.2140/gt.2007.11.215

英文摘要：

We refine the Whitehead torsion of a chain equivalence of finite chain complexes in an additive category $\bA$ from an element of $\widetilde{K}^{iso}_1(\bA)$ to an element of the absolute group $K_1^{iso}(\bA)$. We apply this invariant to symmetric Poincaré complexes and identify it in terms of more traditional invariants. In the companion paper [1] (joint with Ian Hambleton and Andrew Ranicki) this new invariant is applied to obtain the multiplicativity of the signature of fibre bundles mod 4.

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