Burghelea, D.; Friedlander, L.; Kappeler, T. Relative torsion for homotopy triangulations. (English) Zbl 0930.57027 Farber, Michael (ed.) et al., Tel Aviv topology conference: Rothenberg Festschrift. Proceedings of the international conference on topology, Tel Aviv, Israel, June 1–5, 1998 dedicated to Mel Rothenberg on the occasion of his 65th birthday. Providence, RI: American Mathematical Society. Contemp. Math. 231, 37-57 (1999). A homotopy triangulation \(\mathop{\underline{h}}\nolimits\) of a closed manifold \(M\) is a pair \((K,h)\), where \(K\) is a finite simplicial complex and \(h:|K|\to M\) is a homotopy equivalence. For a finite von Neumann algebra \(\mathop{\mathcal{A}}\nolimits\) let \(\mathop{\mathcal{F}}\nolimits=(\mathop{\mathcal{E}}\nolimits,\mathop{\bigtriangledown}\nolimits)\) be a flat bundle of \(\mathop{\mathcal{A}}\nolimits\)-Hilbertian modules of finite type with bundle \(\mathop{\mathcal{E}}\nolimits\) and flat connection \(\mathop{\bigtriangledown}\nolimits\), let \(\mu\) be a Hermitian structure on \(\mathop{\mathcal{E}}\nolimits\), and let \(g\) be a Riemannian metric on \(M\). The authors define the relative torsion \(\mathop{\mathcal{R}}\nolimits(M,\mathop{\mathcal{F}}\nolimits,\mu,g,\mathop{\underline{h}}\nolimits)\in R\), discuss its dependence on \(\mu\), \(g\), \(\mathop{\underline{h}}\nolimits\), and exhibit its relationship with the Reidemeister and Whitehead torsion.For the entire collection see [Zbl 0913.00045]. Reviewer: W.Heil (Tallahassee) MSC: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. 57R22 Topology of vector bundles and fiber bundles 46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) 58J99 Partial differential equations on manifolds; differential operators Keywords:relative torsion; homotopy triangulation × Cite Format Result Cite Review PDF