Displaying similar documents to “The Reidemeister trace and the calculation of the Nielsen number”

Realization of fixed point sets of relative maps

Moo Ha Woo, Xuezhi Zhao (2011)

Fundamenta Mathematicae

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Given a relative map f: (X,A) → (X,A) on a pair (X,A) of compact polyhedra and a closed subset Y of X, we shall give some criteria for Y to be the fixed point set of some map relatively homotopic to f.

Applications of Nielsen theory to dynamics

Boju Jiang (1999)

Banach Center Publications

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In this talk, we shall look at the application of Nielsen theory to certain questions concerning the "homotopy minimum" or "homotopy stability" of periodic orbits under deformations of the dynamical system. These applications are mainly to the dynamics of surface homeomorphisms, where the geometry and algebra involved are both accessible.

Nielsen fixed point theory on manifolds

Robert Brown (1999)

Banach Center Publications

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The study of fixed points of continuous self-maps of compact manifolds involves geometric topology in a significant way in topological fixed point theory. This survey will discuss some of the questions that have arisen in this study and indicate our present state of knowledge, and ignorance, of the answers to them. We will limit ourselves to the statement of facts, without any indication of proof. Thus the reader will have to consult the references to find out how geometric topology...

Fixed point theory and the K-theoretic trace

Ross Geoghegan, Andrew Nicas (1999)

Banach Center Publications

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The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus K 0 ) and 1-parameter fixed point theory (versus K 1 ). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.