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Title: Higher Reidemeister torsion and parametrized Morse theory (English)
Author: Klein, John R.
Language: English
Journal: Proceedings of the Winter School "Geometry and Physics"
Issue: 1991
Pages: [15]-20
Category: math
Summary: 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)
MSC: 19D06
MSC: 19M05
MSC: 57Q10
MSC: 57R45
MSC: 57R52
MSC: 57R70
idZBL: Zbl 0807.57026
idMR: MR1246615
Date available: 2009-07-14T08:26:38Z
Last updated: 2012-09-18
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