Higher Reidemeister torsion and parametrized Morse theory. (English) Zbl 0807.57026

Bureš, J. (ed.) et al., The proceedings of the 11th winter school on geometry and physics held in Srní, Czechoslovakia, January 5-12, 1991. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 30, 15-20 (1993).
This paper constitutes a summary of the author’s Ph.D. thesis [The cell complex construction and higher \(R\)-torsion for bundles with framed Morse function (Brandeis Univ. 1989)]. Proofs of the results cited here will appear elsewhere.
The first section is devoted to outlining a means of passing in a continuous way from the space of pairs \((M,f)\), where \(M\) is a compact smooth manifold and \(f\) is a Morse function on \(M\), into a moduli space for finite cell complexes.
In section two the results of section one are applied in special instances to construct a new invariant which is a parametrized analogue of Reidemeister torsion. This invariant takes values in a certain subquotient of higher algebraic \(K\)-groups of the complex numbers.
For the entire collection see [Zbl 0777.00026].


57R70 Critical points and critical submanifolds in differential topology
57R52 Isotopy in differential topology
19D06 \(Q\)- and plus-constructions