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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.\par 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.\par 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. (English) |
