Axioms for a local Reidemeister trace in fixed point and coincidence theory on differentiable manifolds

@article{Staecker2007AxiomsFA,
  title={Axioms for a local Reidemeister trace in fixed point and coincidence theory on differentiable manifolds},
  author={P. Christopher Staecker},
  journal={Journal of Fixed Point Theory and Applications},
  year={2007},
  volume={5},
  pages={237-247}
}
  • P. C. Staecker
  • Published 15 April 2007
  • Mathematics
  • Journal of Fixed Point Theory and Applications
Abstract.We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory. 
The Reidemeister Trace of an $n$-valued map
In topological fixed point theory, the Reidemeister trace is an invariant associated to a selfmap of a polyhedron which combines information from the Lefschetz and Nielsen numbers. In this paper weExpand
Axioms for the fixed point index of n-valued maps, and some applications
We give an axiomatic characterization of the fixed point index of an n-valued map. For n-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopyExpand
An averaging formula for the coincidence Reidemeister trace
In the setting of continuous maps between compact orientable manifolds of the same dimension, there is a well known averaging formula for the coincidence Lefschetz number in terms of the LefschetzExpand
A formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles
We give a formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles in terms of the Fox calculus. Our formula reduces the problem of computing the coincidence ReidemeisterExpand
The homotopy coincidence index
In a survey based on recent work of Koschorke, Klein and Williams, stable homotopy coincidence invariants are constructed using fibrewise methods generalizing the standard construction of the stableExpand
Axioms for the coincidence index of maps between manifolds of the same dimension
Abstract We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the mapsExpand
Axioms for the Lefschetz number as a lattice valuation
We give new axioms for the Lefschetz number based on Hadwiger's characterization of the Euler characteristic as the unique lattice valuation on polyhedra which takes value 1 on simplices. In theExpand

References

SHOWING 1-10 OF 18 REFERENCES
On the uniqueness of the coincidence index on orientable differentiable manifolds
The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index isExpand
Axioms for the equivariant Lefschetz number and for the Reidemeister trace
Abstract.We characterize the Reidemeister trace, the equivariant Lefschetz number and the equivariant Reidemeister trace in terms of certain axioms.
On the uniqueness of the fixed point index on differentiable manifolds
It is well known that some of the properties enjoyed by the fixed point index can be chosen as axioms, the choice depending on the class of maps and spaces considered. In the context ofExpand
A generalized Lefschetz number for local Nielsen fixed point theory
Abstract Let X be a connected, finite dimensional, locally compact polyhedron. Let f : U → X be a compactly fixed map defined on an open, connected subset U of X , and let H be any normal subgroup ofExpand
The Lefschetz-Hopf theorem and axioms for the Lefschetz number
The reduced Lefschetz number, that is, where denotes the Lefschetz number, is proved to be the unique integer-valued function on self-maps of compact polyhedra which is constant on homotopy classesExpand
A Lower Bound for the ?-Nielsen Number
Abstract : This paper is concerned with the number of solutions of three kinds of equations. Let f,g : X approaches Y and h : X approaches X be maps, and let y sub 0 be a member of Y. The equationsExpand
Coincidence theory
  • R.F. Brown, editor, The Handbook of Topological Fixed Point Theory, pages 3–42. Springer
  • 2005
Coincidence theory
  • R.F. Brown, editor, The Handbook of Topological Fixed Point Theory, pages 3–42. Springer
  • 2005
Coincidence theory The Handbook of Topological Fixed Point Theory
  • Coincidence theory The Handbook of Topological Fixed Point Theory
  • 2005
The Coincidence Nielsen Number on Non-Orientable Manifolds
...
1
2
...