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.

EUDML-ID : urn:eudml:doc:221611
Mots clés:

@article{701784,
     title = {Higher Reidemeister torsion and parametrized Morse theory},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1993},
     pages = {[15]-20},
     mrnumber = {MR1246615},
     zbl = {0807.57026},
     url = {http://dml.mathdoc.fr/item/701784}
}

Klein, John R. Higher Reidemeister torsion and parametrized Morse theory, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1993), pp. [15]-20. http://gdmltest.u-ga.fr/item/701784/