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The lefschetz function of a point

Part of the Lecture Notes in Mathematics book series (2803,volume 1411)

Abstract

Associated to an isolated periodic point of a continuous self map on a manifold is an invariant called the Lefschetz function. It is a formal power series which encapsulates the values of the Lefschetz index of the fixed point for all iterates of the map. We prove that for a homeomorphism of a manifold of dimension at least three any formal power series with integer coefficients and leading term 1 can be realized as the Lefschetz function of a fixed point.

Keywords

  • Periodic Orbit
  • Periodic Point
  • Boundary Component
  • Formal Power Series
  • Infinite Product

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. M. Brown, On the index of Iterates of Planar Homeomorphisms, preprint.

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© 1989 Springer-Verlag

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Franks, J., Fried, D. (1989). The lefschetz function of a point. In: Jiang, B. (eds) Topological Fixed Point Theory and Applications. Lecture Notes in Mathematics, vol 1411. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086443

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  • DOI: https://doi.org/10.1007/BFb0086443

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51932-4

  • Online ISBN: 978-3-540-46862-2

  • eBook Packages: Springer Book Archive