Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T01:10:45.906Z Has data issue: false hasContentIssue false

Reidemeister torsion and Morse–Smale flows

Published online by Cambridge University Press:  19 September 2008

Héctor Sánchez-Morgado
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria C.P. 04510, México D.F., México

Abstract

For several types of stable flows φ and representations ρ of the fundamental group of the underlying manifold, R-torsion for ρ can be computed from the periodic orbits of φ. However, there are counterexamples and the purpose of this paper is to describe the role of heteroclinic orbits in such counterexamples.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Conley, C.. Isolated invariant sets and the Morse index. Conf. Series in Math. 38 (1978).Google Scholar
[2]Floer, A.. Witten's complex and infinite dimensional Morse Theory. J. Diff. Geom. 30 (1989), 207221.Google Scholar
[3]Franks, J.. Morse-Smale flows and homotopy theory. Topology 18 (1979), 196215.CrossRefGoogle Scholar
[4]Fried, D.. Counting Circles. Springer Lecture Notes in Mathematics 1342 (1988), 196215.Google Scholar
[5]Fried, D.. R-torsion for nonunitary representations. Unpublished notes.Google Scholar
[6]Wilson, W.. Smoothing derivatives of functions and applications. Trans. Amer. Math. Soc. 139 (1969), 413428.CrossRefGoogle Scholar